It would be useful for pulling back pages that have fallen off the internet and are not in the wayback machine.

Thats a use case I have hit a few times. I even started backing up useful posts just in case they died.

http://gigablast.com/rants.html is an example. Its a really good insight into the creation of a search engine which really should be preserved.

One that did dissapear but has since come back is this post http://widgetsandshit.com/teddziuba/2010/10/taco-bell-progra... which I went looking for a few years ago but had dissapeared from all search indexes.

Pinboard offers an archival account (25$ a year) that works wonderfully for this. Take a look if you don't already know it.

https://pinboard.in/faq/#archiving

What does indexing mean here? I'm not sure what it means to 'index' but not 'store' webpages as the frontpage says.

I assumed they meant that they extracted meta-data about the page (page mentions "Winnie the Pooh" for example, like a book index) and kept that associated with a key (eg URL) but didn't actually store the content per se. I was hoping the answer to my question would include that sort of detail - what's stored and where.

That's exactly right. The indexed content is stored (as an inserted index) but not the plain text.