Shares are what you're sending to the pool. It's the result of the hashing calculation. The diff you get from the pool is a share value threshold below which cgminer doesn't bother to send that share to the pool. This keeps down traffic, since if a pool accepted every value-1 share bandwidth requirements would be through the roof with modern high-hashrate miners. Your returned shares could have a value in the millions or billions; this is statistically unlikely but it does happen on occasion. The more hashrate you have, the more likely you are to return higher shares, so the higher the pool's discard threshold gets. Every share is weighted by that threshold and summed up (that's the "A" field in cgminer's display, means Accepted), and that's what is used to determine your mining payout because it's a representation of how much work you're doing. Shares are all weighted by that diff value but every individual share could have a different value (which is reported in cgminer when a share is accepted). The only share that actually matters is the one over network difficulty, which is the one that makes a block. The rest are just used to divvy up the block payout to everyone in the pool.

So "shares" is the total number of shares you've submitted, "bestshare" would be the highest-value share you submitted in the current round (?) and bestever would be the highest-value share ever submitted under your mining account. They're not really used for any payout calculations or anything (except total shares, indirectly), but some people like to know that info.