Definition
In pool mining, a share is a hash that meets a lower difficulty target set by the pool (not the full network difficulty). Shares prove that a miner is doing work, even though most shares are not valid blocks. The pool uses share counts to proportionally distribute rewards when a member eventually finds an actual block.
Share difficulty is adjusted by the pool to balance communication overhead: too easy means too many shares submitted, too hard means infrequent proof of work. The optimal share rate is typically several shares per second per miner.
In Simple Terms
A partial proof of work submitted to a pool to prove your miner is working. Used to calculate your reward share.
A proof of work submission from a miner to a pool that meets a lower difficulty threshold than the actual network difficulty. Used to measure each miner's contribution.