Earnings Per Share or EPS is a measure of profitability just like the name itself.
There are lot of qualifications when computing this number but a simple computation is dividing the net profit by the outstanding shares at end of the period. As we have said it is an indicator of the companies profitability. It is a allocated share on the company's earnings to each stock. This number gives you an idea of the companies possible dividend. also by reverse computing you can compute the total net income by multiplying this number to the outstanding number of shares.
In the same way when choosing to invest one might just focus on the number itself, which is unwise. For example you are interested in two companies which has the same EPS. So you are undecided which to put your money on. Though this two companies have the same EPS by reverse calculation one can determine which company is generating income from capital efficiently. The better company is the one with lesser outstanding shares. Let say both has an EPS of 10 and Company A has 10,000 outstanding and Company B has 1,000. So in this case Company B is more efficient because it is able to potentially give its 1,000 shareholders 10 pesos dividend with a smaller capital investment.