The term is so new that there's no accepted definition, particularly since Dell (!) failed to trademark the term.
Essentially the idea is similar to that of a utility - you want electricity, but you don't care which power station supplies it because there's a network supplying electricity to everyone, and you can just tap into it. Which works for electricity, but the Internet isn't quite that sophisticated just yet. But that's the Vision.
Amazon's S3 service just provides disk space, and it doesn't care who uses it or where they are located in the world. Certainly Google's office tools (and Microsoft's web offering) offers a service, not a particular machine, which will look after your application needs. Again, you can create and work with a spreadsheet but you don't know where that spreadsheet is stored, or which machine it runs on - just that it's available when you want it.
Web 2.0 is another term struggling to find a definition, but you can imagine your spreadsheet using calculations which are embedded in another machine somewhere, and storing results of its calculations on Amazon S3. Boundaries are fading away at this point.
Because it's available wherever you log in from, it could be accessed from anywhere in the world. It's "in the cloud" because it can be seen from anywhere (not a good analogy, but ...)
