At the end of the Second Age, the Valar basically didn't know what to do with the 'part-elven' men (or part-human elves), so they gave each of these the choice of which race to belong to. Elrond, Elros, and the children of Elrond were given this choice. Elrond decided to become Elvish, while Elros decided to become Human. From this time on, the choice was final and complete. If you checked their DNA, it would be identical, but in every way Elros was human and Elrond was elvish. Elros and his descendents were given a longer life span than other men, but this was due to a gift from the Valar for their valour against Sauron, and not because of their elvish ancestors. Aragorn can trace his lineage back to Elros, and therefore also has a longer life (he is 76 when LotR starts, I think, and he lives to be about 200). When Arwen decides to remain with Aragorn, she also become completely mortal.
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