The Philosopher's Stone is known from the general public only through legends. The Stone is said to change all metals to gold, and to be needed to brew the "Elixir of Life" which makes its drinker immortal. Producing gold and healing and rejuvenation can in fact be achieved temporarily with transfiguration, and permanently using the Stone.
The Stone's origin is unknown.
Perenelle then publicly claimed (under her fake identity Nicolas Flamel) to have made the Stone herself. She used it for her benefit and that of a few other wizards in exchange for services, while never revealing the true properties of the Stone.
Harry then planned to open an hospital where he would use the Stone to give health and long life to as many people as possible.
The Stone can make one transfiguration permanent every three minutes and fifty-four seconds.