The Elixir of Life is a potion with extend's the life of the drinker, if drank regularly, and is created using the Philosopher's Stone. Nicolas Flamel, the only known maker of the Philosopher's Stone, lived to a great age of 665 using the elixir, and his wife Perenelle Flamel, lived to 668, three years longer than Nicolas, also using it. As it also has the ability to grant a bodiless but earthbound creature a body, Quirinus Quirell attempted to steal it to give the returned Lord Voldemort a body (something which he lacked after being supposedly killed). The Philosopher's Stone was destroyed in 1992 with Nicolas and Perenelle's blessing and their stocks of elixir gradually depleted. They both died later that year.
 Powers, Limitation and Creation
The Elixir of Life grants immortality to the drinker, although it doesn't truly grant immortality, just extends the drinker's life indefinitely, until consumption of the elixir is stopped. It is also able to grant a bodiless but earthbound creature a body, although it is unknown if their are any drawbacks or limitations to this. The frequency of consumption to prevent death is unknown, as is the recipe for creation (of the Philosopher's Stone). It is also unknown whether the elixir stops or slows the ageing of the drinker.
 Appearance and Characteristics
Being an elixir, it, by definition, is sweet, although it is unknown whether this elixir is sweet or not. Nothing is known about the appearance of the Elixir of Life.
 Harry Potter and the Philosopher's Stone
As implied in the title, the stone is a key plot element in the first book, and the elixir is mentioned once or twice too. The stone first appears as the shabbily wrapped parcel in (and the only object in) Vault 713 of Gringotts, though at this point, the reader/viewer should not know what the parcel is, unless they have seen the movie or read the book once before. Rubeus Hagrid, bringing Harry Potter with him, entered the vault holding the stone and removed it under Albus Dumbledore's orders. It was then taken to Hogwarts for better protection (Hogwarts is probably the only place more well protected than Gringotts, this being stated by Hagrid in the first book). Later in the day, Vault 713 was broken into, by Quirinus Quirell (though again, the reader or viewer should not know who broke in at the time). Further in the story, Nicolas Flamel is mentioned, on the Albus Dumbledore Chocolate Frog card Harry receives on the train journey to Hogwarts. The stone is again mentioned when Hermione Granger tells Harry Potter and Ronald Weasley that she read about Flamel and the stone once in a book she took from the library for a bit of light reading. It's final appearance is near the end of the book, in which Harry defeats Quirell and thwarts Voldemort's first attempt at returning.
 Extra Information
It is unknown whether the elixir stops illness and injury, or whether it just prevents death from old age.
In the movie it is not mentioned that the elixir can provide Voldemort with a body.