What does "accepted shares" mean?

An accepted share represents work that your miner did towards a round in a mining pool.

When the pool finds a block, it distributes the block reward (i.e. 25BTC) to the miners according to how many shares they have contributed during that round. The more shares you contributed, the more payback you get.

It is simply a way to keep score, and to attribute the reward proportionally to the amount of computing power that each miner contributed to the pool.

Edit: "accepted share" is one which is valid at the time the pool receives the work from the miner, but sometimes the work arrives too late and a new block has replaced the previous one. In these cases you will have some "invalid shares" which don't count towards the revenue share.