Glutamine is an amino acid, one of the most common found in the human body (you will also see it referred to as L-glutamine). It is classified as a non-essential amino acid, meaning that the body can manufacture it. Glutamine has many functions in the body; DNA synthesis, protein synthesis, assisting immune cell production, among the many, many functions. For fitness and weight loss, glutamine helps rebuild muscle tissue damage brought on by training, mitigates cortisol effects, both of which aid post-training recovery.
Under ordinary conditions, glutamine levels can be sufficiently replaced through normal dietary means. Glutamine is found in virtually all meats, eggs, many dairy products, beans, and several vegetables. However, when one is engaged in extended physical activities, glutamine levels drop faster than ordinary eating can replace them, and this is a period when the body can really use more glutamine - to offset cortisol catabolism and aid muscle rebuilding.
This is why you would take glutamine supplements. Immediately post workout, the most common practice is to take 5 to 10 grams of glutamine. Some people will also take glutamines prior to sleeping as well. On non-training days, again you should take glutamine just before sleeping, because sleeping is when tissues are built and repaired the fastest.
In my research, and in my own experience, I have found no harmful effects either from prolonged glutamine usage or from taking higher doses of glutamine supplements, though excessive glutamine consumption will probably have no beneficial effect either.