Earnings Per Share are the amount of accounting profits per share. After all costs have been taken into account, including taxes and non cash items such as Depreciation and Amortisation, you are left with Net Income, or Earnings. When you divide this amount by the Number of Shares Outstanding, you are left with the amount of Earnings Per Share.
It is an important figure for many investors as it tells you how much the company is earning in profit for each share you own. Looking at this figure on a ‘Per Share’ basis makes taking into account the effects of additional shares issued easy.