Lord Restimar was one of the Seven lost Lords and a Telmarine Lord who opposed the usurper Miraz. These lords did not fear the oceans or forests, unlike most Telmarines, and were of the few who respected the legends of Old Narnia, or Narnia before the invasion from Telmar.
Restimar and six other lords were sent to "explore the seas beyond the Lone Islands" by Miraz, who did this in an attempt to be rid of them.
On his journey to the eastern end of the world, King Caspian X visited an island (which he and his crew later named Deathwater Island) and found what was at first thought to be a golden statue at the bottom of a pond. After Edmund's shoes were flecked with splashes of the water, which turned them to gold, the company realized that the water turned things into gold, and determined that the "statue" must in fact be one of the missing Lords.
Besides that pool, there was no other water on Deathwater Island, and obviously it could not be drunk. Restimar must have been hot with thirst, and then came upon what he thought was a harmless pool of water, so he undressed and jumped in, never realising the danger it represented.
In the 2010 film version, Lord Restimar had fled to the Lone Islands to escape Miraz, along with his 6 fellow Lords. Once there, they learned of the Green Mist that was abducting people. They all swore a pact to find the source of the Mist, and destroy it.
Restimar made it as far as Deathwater Island, which in the film was also Dragon Island, where he and Lord Octesian died. Judging by what was seen in the film, the fate of Lord Restimar seems exactly the same as it was in the book, with the small exception that he seemed to have accidentally fallen into the pool instead of deliberately.