In barbershop parlance, a "line up" is a partial haircut typically performed on a black patron.
One feature of many African American haircuts is a very very hard line at the forehead, temples, around the ears and the back of the neck. Especially when the hair is in an extremely tight curl, tapering effects and so forth lead to a nice greyscale graduation in tones, and a clear demarcation of where hair begins and ends.
Regardless of whether the hair is tapered or all one length, many a customer of color wishes to see a "finish" on the hair cut in which the boundary line between hair and skin is razor-sharp, and deeply defined: so typically at the end of the haircut, this type of service is performed. However, given that hair grows, if the customer wishes to keep that level of definition in his haircut, he or she will typically require that this process be repeated, even if the hair otherwise has not grown out enough to warrant a full haircut.
The vernacular is a "line-up", and it typically costs far less than a full haircut.
The usual rules apply: the customer is caped with a neck strip and prepared as if for a haircut. But the hair is typically shorn only around the hair boundary: starting in the middle of the forehead and working towards each temple, working down the temples towards the ears, working around the ears and towards the back of the neck, and the neck itself. A "liner" clipper is used for this purpose, which does very fine cutting, and is typically adjusted to the point where too much pressure will actually nick the skin. Brushing the hair so that it lies low first augments the sharpness of the line. Typically all the hairstyle/haircut decisions as to where to define the sideburn, and whether to round or square the back of the neck (irrelevant if the haircut fades to skin well before the neckline) have already been made, so it is literally just going back over the lines with clippers and redefining them.
To truly finish the haircut, many customers insist on a razor being used to shave the skin completely right up to that boundary line. For this purpose shave oil, shaving cream or similar lubricants are used: but some barbers actually use a form of hairspray- because it gives a visual feedback of where the razor has been. It also leaves a chalky white line at the hair boundary - which leads some folks to believe that some guys draw a white line with a chalk pencil around the perimeter.
Beards are often "lined up" as well, usually for a small additional charge.
When it's done right, the hair literally looks like someone's taken a scalpel and a ruler and made a hard, firm cut between hair and skin. It's a beautiful effect. And a man doesn't have to have short hair to do it either: some men with dreadlocks or otherwise long hair will choose to have the face, neck and temples "lined up".
Once you've done these, or know that they're done, you suddenly appreciate why certain men look more "polished" than others, and as to why there is such a culture to get constant haircuts even if the bulk of the hair doesn't require it. It is just what you do before going out to the job interview, to the church service, or the club.