There are two kinds of immortality that I can see:
1)Not able to die at all -- ie, you could be at ground zero in a nuclear blast and survive. A subcategory is things like vampires or "Highlanders" (from the movie) who can only be killed in specific ways, like a stake thorugh the heart of having their heads cut off.
2)Will not die of natural causes -- this is better defined as "indefinite life." You could theoretically live forever, barring nasty incidents. This is intriguingly possible for us humans.