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The idea of Circulate is that a group of dancers who are arranged along a path will each move forward one position along that path. For example, in a box, there are four positions, and there is a natural path that goes through all four positions.
Some people find it helpful to think of this path as being like a railroad, with the positions corresponding to stations, and the dancers corresponding to trains. As with a train on a railroad track, the dancers can only move along the path. The path itself may be curved, but the dancers must stay on the path, and they can only go forward or back along the path. They can't move "sideways", off the path.
For a particular path, each dancer has only one possible "next position" -- the next one along the path in the direction that he or she is facing. Also note that since the path is closed, connecting back on itself, if a dancer circulates enough times (in this example, four times), that dancer will arrive back at his/her original position.
In parallel waves, each wave has two centers. The four dancers who are centers of a wave are also considered to be the centers of the whole formation. These dancers form a box, and they can circulate in that box. This is a Centers Circulate.
The four other dancers are considered to be the ends of the whole formation, and they also have a circulate path (which can also be viewed as a box, just a very wide one). So they can do an Ends Circulate.
These two paths can also be identified in other ways. For example, if all the dancers in the center box are boys, the caller might say Boys Circulate, and the meaning would be exactly the same (in that situation) as Centers Circulate.
These two paths also exist in any sort of parallel lines, such as parallel two-faced lines, and calls like Ends Circulate and Girls Circulate apply in the same way in those cases.