Amino Acids are the constituent components of protein. Although a high level of protein is recommended for both muscle gain and fat loss (due to its muscle sparing and appetite satiating effects) there are certain instances when the addition of free form amino acids is desirable.
Most often this can be to provide the body with extra levels of the Branched Chain Amino Acids (BCAA), leucine, isoleucine, and Valine, or to supply the amino acid Glutamine which has been shown repeatedly in various studies to have recuperative effects above and beyond just increasing protein intake. Glutamine and BCAA's have been shown to have a beneficial effect particularly in the case where athletes are dieting, or otherwise facing substantial stress.
Amino acids can come in tablet form for convenience, or as powders, where they are usually added to a protein drink. Regardless of the form, many athletes consider amino acids a vital part of their nutritional protocol.
A special type of amino acid is Beta-Alanine which has been used extensively in athletes to enhance training adapatations. The article below on Beta-Alanine shows how this can be used.