The link provided earlier pretty much explains what back-drilling is, but a brief example might help. If you had an 8-layer board, and a through via made a circuit connection only between, say, layers 2 and 3, then the rest of the via isn't needed for the circuit. One of the major impacts of a via, in high-speed circuits, is the capacitance (and inductance) that it adds to the signal path. So that big unused portion of the example via that passes through layers 4-8 is adding nothing but parasitic capacitance to the circuit. For very high-speed circuits this can compromise signal integrity. Back-drilling removes the unused portion of the via. The only way to determine if back-drilling is required is to do a high-end simulation of the physical circuit layout. (Or to build the board without it and see what happens.)
