From Princeton WordNet:
S: (n) pagination, folio, page number, paging (the system of numbering pages)
That explains the whole shebang. Basically: Take anything arbitrarily long and split it into pages.
An unpaginated file, although I've never seen one, would be just a stream of content, whereas a paginated one would obviously consist of a countable number of pages.
Take a browser showing an HTML page as an analogy: It's unpaginated. When you decide to print it, it becomes paginated because of the way our printers work and we humans choose to read nowadays. The tricky part of course is defining where pages should start and end, and the fact that with the pagination, you create logical or physical boundaries that weren't there before.
Then again, the problem with working with unpaginated content is that most current software is based on pagination, from Word to Acrobat. PDF does not seem to support this. DjVu might, although I didn't find a proof and I'm not experienced with DjVu itself.