Stands for 'Earnings Per Share'. Simply the earnings of a company divided by the shares in issue. Needed for the P/E calculation. If 100% of the profits of a company were distributed to shareholders (dividend) then this would be the gross amount payable.
Take all this year's profits of the company and split it between all the shareholders. This is how much each shareholder would be due. Important? - Yes for the deep and meaningful type, but it really doesn't give you a better argument than just referring to plain old profits or earnings.