Amino Acids are essentially the building blocks of life. Your DNA is made up of amino acids. All proteins and enzymes are made up of amino acids as well. You can ingest proteins (in all forms) to get extra amino acids for your body to break down and then reform into the proteins and stuff that it needs.
Some manufacturers add extra amino acid mixes to their whey protein. Thats because whey protein (as a milk product) has 8 amino acids - which happen to be the exact set of amino acids that your body uses to build and repair muscle tissue. There are, however, over 300 amino acids (one source said 500) - only 20 to 22 of which are used by living things. Since only 8 are in whey, some manufacturers add extra. Since those extra amino acids are not used for making muscles you would have to look up the specific acid to find out what it did.
Of those 20something amino acids, 8 are essential - which means that they cannot be synthesised by the body enough to be used and therefore must come from food. Conditionally essential AA are only sometimes this way - like if you are lacking a certain metabolic process or at a certain time in your life.
If you are looking at this from a bodybuilding standpoint the extra amino acids that you get from protein shakes and eating extra protein will allow your body to build bigger muscle without dipping into its reserves. Another thing to consider with supplements are BCAA or Branched Chain amino acids. They are 3 of the amino acids that have a specific structure (a branched structure) and make up 1/3 of your skeletal muscle mass. Some products will add extra BCAAs.
Honestly, I love the idea of getting my amino acids from food sources whenever possible (rather than a laboratory) so whey protein is the best thing for building muscle - in my opinion. Just be sure you are using a high quality, chemical free whey!