Earning per Share ratio (EPS)
EPS is simply the earnings (e.g., profits) of a company divided by the outstanding shares of its common stock.
Say a company makes $100 in profits and has 100 shares. Here the EPS of this company is $1.
You could look over time to EPS to see how well a company is doing, or you can compare among companies in the same sector, to see if by comparison the company is doing better or worse.
The index could be more precise by adding any diluted shares or preferred dividents [e.g., basically agreements the company has that could be turned into shares (e.g., a debt that can be paid with shares)] leading to:
The overall expectation is that if EPS within a company increases, or is higher than other companies in the same sector, the stock price will increase. One would expect traders will be willing to pay more for such a good company.
That conclusion is not bullet proof, price may go up in low or lowers EPS, if on the eyes of analysts, EPS should have been even worse.