A sink overflow is a small hole on the backside of the sink. It diverts rising water back into the drainpipe so that your sink doesn't overflow. The overflow also helps your drains work more efficiently as it allows air into the plumbing pipes.
So now you know what all those pesky holes are, but how do you clean them?
This is a tricky one and it varies from state to state and building code to building code. Your best bet will be to check in with your county inspector BEFORE you buy your tub.