Evolution

[simplexity]

Variation is due to mutation. Natural selection determines which mutations are most beneficial in the current setting. Variation can be caused by mutations (which are rare). But as you've mentioned natural selection filters what mutations are passed down. Nevertheless there are limitations on the amount of variation (this is well documented). See my previous post for links.

Actually mutations are anything but rare. They happen all the time while any living thing is well... living. It is just an aspect of life. Your cells are being bombarded by any amount of things all the time and during any replication errors are made. Granted beneficial mutations may be rare but when they do happen and the genes are passed on, this is exactly how a species evolves.