Basic Earnings per share (Basic EPS) tells an investor how much of the company's profit belongs to each share of stock. If company ABC reported earnings of $100 million dollars and had 20 million shares outstanding, the basic EPS would be $5 ($100 million earnings ÷ 20 million shares outstanding = $5 per share). The figure is important because it allows analysts to value the stock based on the price to earnings ratio (or p/e ratio for short).
Basic EPS are not as accurate as Diluted EPS.

What are Diluted Earnings Per Share?

Diluted earnings per share (Diluted EPS) takes the basic earnings per share figure one step further. Basic EPS only takes into account the number of shares outstanding at the time. Diluted EPS, on the other hand, estimates how many shares could theoretically exist after all stock options, warrants, preferred stock and / or convertible bonds have been exercised.
The theory goes that because some or all of these investments could be converted or exercised, the number of shares outstanding could increase at any time. This reduces the amount of a company's earnings each share is entitled to. In doing so, the price to earnings ratio becomes higher, and the stock appears more expensive.
In most cases, the diluted earnings-per-share figure is far more accurate estimation of the total earnings per share and receive special attention when valuing a company.