Verification is the computer checking to see if the disc matches what the computer should have burnt. If you burn at high speeds then you should verify; if you burn at slower speeds then you may not need to. (Speed here is relative to the media's rated speed. You may have a 52x burner, but if the disc is only 32x and you burn it at 16x it should come out error-free. That being said, it is fairly rare for a disc to fail verification in such a way that it is unusable.)
yea, verification is just that, it verifies that all data was written without error. I've written data before and had the verifcation fail on me, usually because I was writing onto a crappy disk at a high speed. In general you're going to want to let the verification happen, because if it comes back with an error and you were backing up something important, that's your cue to chuck the cd/dvd that you just burnt and make another one, and make sure it passes verification. Otherwise certain items could be unreadable/corrupt etc.