The Elixir of Life is a potion which extends the drinker's life, making him or her immortal as long as the Elixir is consumed regularly. It can only be made with the Philosopher's Stone. In Harry Potter and the Philosopher's Stone, Voldemort attempts to acquire the stone in order to create the Elixir, so he can have eternal life.
The only two people who have been known to drink the Elixir of Life are Nicolas and Perenelle Flamel.
From the Story
"The Elixir of Life, which turns the drinker immortal, can only be made using the Philosopher's Stone.
Voldemort plans to steal the Philosopher's Stone in order to make the Elixir of Life; he hopes to make a new body once he is able to make this potion."