Not that I trust Wikipedia farther than I can throw them, en.wikipedia.org/wiki/Doughnut suggests that they were originally little ‘nuts’ of dough, kinda of like what are called donut holes in the US. This surprises me because I thought the ‘nut’ was a contraction of ‘nought,’ or zero (as in little zero shaped things made of dough.

Either way, apparently the hole is for the same reason as with bagels–if you just make a disk of dough, the center will cook at a different rate than everything else.