I have a wordpress installation that I look after (in fact its phpwomen.org) and since upgrading it to 2.7 I see that it has lots of "click here to upgrade" buttons, both for the core code and even to upgrade and install plugins. However when I click on these, either the core upgrade or to install/upgrade a plugin, I get prompted for my FTP details.
I found this odd, as I thought I was downloading and unpacking a file. I read around and there isn't much information about this feature at all. It seems like such a useful thing if it would work, then I can give someone an admin login and they can just work everything from there without me giving them shell access. After a very frustrating few weeks of trying, I found out the answer.
WordPress can update without FTP
I don't need to install FTP on my server (good, I don't want to), I had incorrect permissions on my files. When the user that apache runs as can write to the wordpress directories, then the upgrade stuff all just works! The FTP credentials are for if the web server doesn't have the right information, then wordpress prompts you for your FTP details, and attempts to use those to FTP back to the same server it is on to be able to write the files it needs. As wordpress is often used in a shared hosting environment, this makes more sense than I first thought.
I really hope that helps someone, I spent ages being confused over this "feature"! If you have any more details or information, or if this works for you, then please add a comment below :) I'm off to enjoy my new wordpress feature ...