Shares outstanding is issued shares minus treasury-stock. It is larger than float, because it includes locked-up insider and strategic holdings. Multiply it by the price and you get market-cap; divide net income by it and you get eps.
Share count drifts constantly: up from stock-based-compensation and offerings, down from a share-buyback. A company whose share count grows 4% a year needs 4% earnings growth just to keep EPS flat.
Example: net income is $480M on 240M shares, so EPS is $2.00. The company issues 12M shares for an acquisition. On 252M shares the same income gives $1.90, a 5% hit before any business change.
Related: float, market-cap, eps, treasury-stock