SPOILER ALERT

The basic idea is this: If the physical world (including consciousness) is just a succession of states, then why would it matter that these states occur sequentially in time and at the same place? The Dust Theory is the idea that it doesn't matter -- that the same collection of bits that describes the universe we experience also describes some ridiculously large number of other universes.

There's more on Egan's site, although it might be hard to follow if you haven't read the book:

http://gregegan.customer.netspace.net.au/PERMUTATION/FAQ/FAQ.html (edit: linked in TFA, I see now.)

The book is excellent, by the way.