Imagine that the buffer is divided up into contiguous, non-overlapping runs of text such that no extent starts or ends within a run (extents that abut the run don’t count).
An extent fragment is a structure that holds data about the run that contains a particular buffer position (if the buffer position is at the junction of two runs, the run after the position is used)—the beginning and end of the run, a list of all of the extents in that run, the merged face that results from merging all of the faces corresponding to those extents, the begin and end glyphs at the beginning of the run, etc. This is the information that redisplay needs in order to display this run.
Extent fragments have to be very quick to update to a new buffer position when moving linearly through the buffer. They rely on the stack-of-extents code, which does the heavy-duty algorithmic work of determining which extents overly a particular position.