L, I'm sure someone will be along with a more informed answer but, in short , you're safe. Java is ubiquitous, it's everywhere, from your pc to your phone and your video recorder. It's a platform independent language (and probably a lot more too). If you want to check if you already have it go to uninstall programs, it'll show there. If you don't trust the java popup, Google java download, it will take you to a Sun site (the hardware / software company, not the "news"paper!
You do need to update from time to time, it's prone to being "exploited" like any almost software.
ps, if you right click (from the uninstall panel) on Java and select open you can see a set of tabs. The Update tab allows you to choose how frequently Java checks automatically for updates. That should reassure you that it is genuine.
I'll second that. In short, just update it. (It should have a hot cup of something (Java lava is it?) with swirls above it as the logo.)
It is just a language devised by Sun Microsystems to allow programs written in it to run on multiple devices. It is deliberately restricted in what it can do to your computer. Some websites have small Java "applets" on them to provide functionality that you can't get with a normal browser software. (e.g web cam control, control of a scanner through a browser, etc.)