Any time a player on offense moves after the team sets in its formation, but prior to the snap, there is a man in motion. A man in motion is most often a player going from one side of the formation to the other, but it can take on a number of different variations. Teams will regularly use a man in motion to determine the type of defense that the opposing team is in, since the opposing team will have to adjust its defense based on where the man in motion goes.
Offenses use a man in motion for a variety of reasons prior to the snap. Its primary use is as an indicator to determine what type of defense the opposing team is in. A quarterback will know what the opposing team is trying to do based on how it adjusts to the motion prior to the snap. Another reason a team will use a man in motion is to set up its play. Teams will often come out in a slightly different formation than they wish to use to keep the defense from reacting too early to the play that they wish to run. The late motion will set up the proper play.