The following, from an ACLU website, are examples of the practice as it is unjustified: 
 

And the following, from a website of the Police Executive Research Forum, further discusses and describes the practice as it is unjustified, and the passage quoted offers policy guidelines to prevent it: 
 

Part B then goes on to give procedures (e.g., acting courteously in various ways) intended to prevent perceptions of biased policing.  For purposes of this paper, I am only interested in the concept of biased policing or racial profiling, not in the perception of it.  Perception of biased policing is an important issue in itself, but a separate one, since appearances can be deceiving in either direction.  That is, racial bias can appear not to exist in a particular incident even when it does, and it can appear to exist in a particular police incident even though it is not actually a causal or motivating factor in that incident. 

Notice the ACLU says that: "Racial profiling" occurs when the police target someone for investigation on the basis of that person's race, national origin, or ethnicity.  And the PERF policy is very similar when it says: Race/ethnicity can never be used as the sole basis for probable cause or reasonable suspicion.

However, the PERF policy goes on to say that "Officers may take into account the reported race or ethnicity of a specific suspect or suspects based on trustworthy, locally relevant information that links a person or persons of a specific race/ethnicity to a particular unlawful incident(s)." 

This essay is an attempt to distinguish when racial profiling might be justified from when it is not, or in the PERF terminology to distinguish between using race/ethnicity as the sole basis for probable cause or reasonable suspicion on the one hand and, on the other, using it as legitimate information to link someone of a specific race or ethnicity to a crime, or to a planned or seriously contemplated crime. 

Notice first, however, that knowing what racial profiling is does not necessarily allow you to know when it occurs.  There will be cases where police can say the evidence they had available is what caused them to stop a particular person when in fact that was not the actual reason they stopped that person.  Insofar as racial bias is an internal psychological motive, it is, in particular cases, often difficult to be able to prove or identify.  In some cases a policeman may not know him/herself whether s/he was operating under a bias or made a legitimate deduction.  Nevertheless, it is important to know what constitutes racially/ethnically biased policing. 

Also, one cannot tell merely from certain kinds of police encounter statistics (though one might have a reasonable suspicion) whether the police are targeting people based on racial motives.  Police patrols in, for example, black neighborhoods would obviously more likely afford more police encounters with black citizens than with white citizens.  And, if for some reason, some ethnic group was more likely than any other to commit certain infractions or if there were more crime in some kinds of neighborhoods than others, it would follow that the percentage of police encounters involving that group's members would be higher than their percentage in the population.  For example, it might turn out that white collar crime is primarily a white male type of activity.  Or if white males have far more access than others to positions that would allow white collar crime, then it would be reasonable for white males to be charged with such crimes in a higher percentage of cases than the white male proportion of the population in general.  In order to see that police are biased in their policing, one would have to see that they do not treat people equivalently under legally relevant similar situations.  If police officers ignore white or white male speeders they see but stop and ticket black or female drivers going the same or even slower speeds, then that is grounds for believing the officers are policing on a gender or racial bias. 

Biased policing is policing that gives preferential treatment to some races, genders, or ethnic groups or that essentially harasses or punishes members of those groups which are disliked or considered to be suspect just because of their race, gender, or ethnicity even though they do not fit a description of anyone who is committing crimes or who has committed a crime. 

First, the general principles are (1) it is not bias if the race, gender, or ethnicity of the individual descriptively narrows the search for a suspect to the same degree, under the circumstances, as would any other characteristic, such as a description of clothing or the make and color of a car, or the first three license plate numerals; and (2), more serious (potential) crimes, and/or (potential) crimes with worse consequences or harm, require less descriptive narrowing of the field of possible suspects than do less serious or less harmful (potential) crimes.  And (3) less intrusive or damaging police activities require less descriptive narrowing of the field of possible suspects than to more intrusive or harmful police activities. 

Descriptive narrowing makes it more likely under particular conditions that the person fitting the description is the person being sought.  What makes a description narrowing is not just the characteristics described, but the likelihood of those characteristics fitting the guilty person in comparison with the likelihood of their fitting others in that situation or environment.  Hence, a description that is narrowing in one environment may not be narrowing in another.  It is not the description by itself that makes it useful for identifying the likely perpetrator of a crime, but the ability of that description to distinguish the perpetrator from others in a particular environment.  The exception or most special case of this is a description which is so unique that it works to narrow the potential of a person fitting that description in any and every environment, which is presumably what finger prints or DNA samples do, or at least what they are alleged to do. 

But in any given environment, various kinds of descriptions might serve to give descriptive narrowing.  For example, if three suspects were fleeing the scene of a bank robbery and were seen to get on a certain highway with all three of them in the front seat of the car, that would be an important identifying clue, I would think, to any policeman monitoring traffic on that highway from that direction where traffic was relatively sparse and where almost none of the cars had more than two occupants.  But it would not be a helpful clue in a commuter car-pool lane during rush hour in a large city. 

Hence, if an ethnic, racial, or gender description is sufficiently narrowing in a particular circumstance, it ought to be allowed as evidence for probable cause, or as justification, to initiate police activity in regard to a particular individual or group of individuals.  In the kinds of cases cited in the ACLU, and similar, reports above, what makes those cases egregious is that the racial characteristics by themselves do not sufficiently narrow the list of possible perpertrators to warrant stopping or following anyone.  And this is compounded by the fact that, or is particularly true when, there is no known crime or any likely crime for which to investigate anyone in the first place.  There is no reason to stop anyone for driving a luxury car if there are no luxury cars of that make reported stolen and if there is not an ongoing epidemic of luxury car thefts in the area. Or, to put it another way, "driving while black" is not by itself sufficient grounds for police investigation under any normal circumstances or in the kinds of environments where the ACLU cases occurred.  But if, in a nearly all white, mostly middle class environment, there is a report of the theft of a luxury car by a black person, or if there have been such thefts by black suspects over time in this neighborhood, of the relatively few luxury cars owned there, it seems to me that the driver of this particular car in this particular case evokes reasonable suspicion, even if he is innocently and only coincidentally in a place where his characteristics happen to meet a description that is sufficiently narrowing under the circumstances. 

As mentioned in the above sentence parenthetically, there are at least two factors to be considered in judging whether the probability is sufficient for police activity to be warranted.  The greater the seriousness or magnitude of harm of the (potential) crime in question, the less the probability should need to be in order to justify police action.  And the less intrusive or less potentially damaging in any way the particular police action is, the less the probability should need to be to justify it.  In other words, whatever the proper range of probability is to justify police actions against a person who fits any kind of description, whether racial/ethnic or otherwise, that range should be narrowed or expanded commensurate with the seriousness of the crime and with the invasiveness and potential harm of the police actions. 

In other words, if the description fits 100 inhabitants in a particular area, police might be justified in questioning or pursuing all of them in regard to the impending setting off of a weapon of mass destruction, but might not be justified in questioning any of them about the pickpocket theft of a wallet containing only $20 in case. 

And in regard to any particular crime, police would be more justified in something like outside surveillance than in a search of their homes or a phone tap, if they cannot narrow the description of the suspect to fewer than the 100 people. 

In order to be morally justified on the basis of the description (whether ethnic, racial, gender, or otherwise in any way), the seriousness of the police activity should be commensurate with the seriousness of the crime and the probability that the description available in a given environment identifies the alleged perpetrator being sought.  The courts can set those parameters, and probably different courts will have slightly different intuitions for them.  But there is no reason to believe that a merely ethnic, racial, or gender description is always insufficient cause for any police activity at all. 

Finally, one news report stated that the Israeli's say ethnic and racial profiling is inadequate and never as effective as other sorts of airport security measures and attention to specific behaviors -- such as airline ticket buyers' answers to certain questions or avoidance of eye contact, etc.  As with many such news reports, the rationale for the claim is not given, so it is difficult to know whether the indicators the Israelis look for are simply very good at ferreting out (potential) criminals or whether racial/ethnic profiling in the Middle East simply does not narrow the field sufficiently, given the large number and percentage of people that would fit the description. The latter might not be the case in U.S. airports or other sensitive facilities.  Clearly if racial profiling would be ineffective, there is no point in using it, but it is far from clear that it is any less effective in catching or deterring (potential) criminals than would be any non-racial, non-ethnic description, trait, or action which narrows the probability of detecting the actual perpetrator by the same degree.