Free Cash Flow is calculated from the Statement of Cash Flows as Cash From Operations minus Capital Expenditures on Fixed Assets. Unlike earnings, it omits purely paper only expenses like depreciation to give a better sense of the cash available to the business.
Free Cash Flow per share should be compared with Earnings per Share in order to understand whether a company is able to turn its earnings into cash or not! Ultimately every company needs to make cash to survive and without free cash flow a company will have to go begging to shareholders or resort to borrowing. The best companies are 'cash machines' - you should look for companies that make more free cashflow than earnings.
N.B. Cashflow can be very 'lumpy' as capital expenditures are not consistent from year to year. Also growing companies may have to invest heavily ahead of cashflow to keep up with demand.