This procedure is done when the aesthetics of your gum line are compromised (such as some people have their gums pulling back from their teeth). The condition called Gum recession is not only cosmetically unappealing (Teeth appear longer) but also functionally problematic.
The gums are designed to cover the roots of teeth which are naturally sensitive and can be easily abraded away by even toothbrushes. Soft tissue is taken from the patients mouth by grafting from a new site (usually roof of the mouth) and used to replace the lost tissue on the affected site.