EPS is an acronym that stands for Earnings Per Share. In effect, there are two types of EPS figures that investors are told about - Basic EPS and Diluted EPS.
Basic EPS is really, really simple. A company takes the profit it earned over a certain period, perhaps a year, and divides it by the average number of shares of stock the company had issued. If the company earned $500 million and had 250 million shares of stock issued, Basic EPS would be $2.00 because $500 million profit divided by 250 million shares = $2.00
Diluted EPS is the same thing except the shares outstanding figure is adjusted to include shares that might or will be issued in the future, such as stock options promised to management. If a company has a lot of future stock to issue, the "real" EPS would be lower than the basic EPS figure would show. Personally, I only pay attention to Diluted EPS. I think Basic EPS is worthless in comparison.
The Reason Basic EPS and Diluted EPS Figures Are Important to New InvestorsWhy is EPS so important? Many conservative investors use Basic EPS and Diluted EPS to calculate how much they think a stock is "worth". Some investors only pay 10x EPS for a stock, which would be a 10% rate of return. If a stock has $2.00 EPS, they wouldn't pay more than $20 per share. Other people pay 8.5x EPS + the growth rate, which was a formula recommended by legendary value investor Benjamin Graham. That is, if a company was growing at 15%, Graham said you probably shouldn't pay more than 8.5x + 15 = 23.5x diluted EPS. For a company earning $2.00 EPS, that would be $47 per share because 23.5 x $2.00 = $47.
Basic EPS and Diluted EPS are also important because dividends are ordinarily paid out of profits. If a company has EPS of $2.00, it can't pay dividends of $3.00 indefinitely! It's just not possible. Dividend investors look at the percentage of EPS paid out as dividends to gauge how "safe" a company's dividend payment is. For more information on this topic, read What Is Dividend Investing?
For a much more advanced discussion, read my essay on Basic EPS vs. Diluted EPS, which are part of the Investing Lessons explaining how to read financial statements.