"To index" means to point, as with your index finger. An index, such as at the end of a book, serves to point into the main body of the work. In this context, I think of an index like a mass noun; the whole thing serves the purpose of pointing, so one does not count the individual entries to quantify the whole. This is the same sense as in database indices, I think.

I don't really make a distinction between "indices" and "indexes"; it seems more a matter of how integrated "index" is into English, since "indices" would be (I believe) the Latin pluralization, while "indexes" uses the more typical English plural scheme. They index (ha) the same semantic meaning in my mind.

(We have the same issue with "appendix" and "appendixes" vs "appendices". It's telling that neither spelling bothers iOS as I type this.)

Then you have octopus with many plural forms: octopuses, octopi, octopodes (oct-oh-pohds, oct-o-po-dees), octopen, octopees, octopa, ...