Earnings per Share, so called EPS stands for a company's net profit divided by the number of shares outstanding. In this way, an investor holding a certain number of shares knows exactly how much of the company's total profit goes to one of his shares.

The logic of the EPS parameter in relation to the share price thus implies that the share price itself is irrelevant unless we relate it to what we as investors get in return for buying it. One of those things we can get in return is precisely EPS. 

The higher the EPS, the more profitable the company, and the lower the share price of that company, the better the investment might be.

Example:

In 2020, McDonald's reported a net income of $4.7 billion and had 745.2 million outstanding shares of common stock. This means that McDonald's EPS for 2020 was $6.30 per share ($4.7 billion divided by 745.2 million shares).

In comparison, in 2019, McDonald's reported a net income of $6.0 billion and had 764.4 million outstanding shares of common stock. This resulted in an EPS of $7.85 per share ($6.0 billion divided by 764.4 million shares).