EPS stands for earnings per share. This is how much of the company's profit they are sharing with stockholders on a per share basis.
Why It's Important
EPS holds a lot of weight when investors are evaluating stocks. I think an example will better illustrate why:
Let's say we hold share of Walmart. As a market (collection of potential buyers), we think Walmart's EPS will be $1.00. Walmart posts their earnings and *shocker* the real EPS is only $0.50. Walmart's stock then goes down because they are not making as much profit as the market thought they were and investors start selling to get out of the bad investment. It also works in the opposite direction. Let's take the same example but they really post earnings of $1.50. Now, the stock will go up because more people are buying. Walmart is more profitable than the market thought.
When evaluating stocks, it's important to see how profitable a company is before you dive in. Profitability is important to the market and can really impact buy or sell decisions.