Board Thread:Lore Discussion/@comment-26861588-20150814151511/@comment-9212235-20150815072320

As has been pointed out in the first comment, Alduin literally eats the world, as seen in The Seven Fights of the Aldudagga. He does not bring about an Apoloclyse as we would understand it. The Eating does not end the world, it resets it. These are called kalpas. There are theoretically an infinite number of them as all possibilites of Anu's psyche are played out within the Dream.

MK explained it once, i believe in his AMA:

''When you consider a place like Tamriel, sometimes it's best to take titles literally. Alduin is the World-Eater. It's not going to be 'the end of all like as we know it,' leaving a barren wasteland of Earthbone dirt... it's going to be the whole of Nirn inside his might gullet.''

As far as his dying... maybe he died, maybe he didn't. Maybe he's just healing in some Aedric realm. Maybe he was destroyed and now joins his counterpart the Void Ghost wandering the nothing.