Fully diluted refers to shares. The fully diluted shares represent the sum of common shares a company will trade after options like convertible and employee stock are exhausted. These shares do not represent the ones currently emitted but the ones which can be obtained through conversion.
Their number is used when calculating a company's earnings per share because they decrease the money earned per share of common stock while increasing the shared basis. This phenomenon might not happen always, but it may be an essential indicator of how many shares will be outstanding in the future. Also, the company's policy concerning conversion is bound to change over time, impacting expectations about the number of fully diluted shares.