SQLite is basically a database to store information for mods (which takes up less space if the plugins just wrote directly to your hard drive).
There's no need to install extra software, which is one of the nice things that differentiates SQLite from other databases. Rather than having to run a database server, SQLite is a library that allows a program to treat a file as though it were a relational database, eliminating the need for extra software. As long as your program (in this case, Bukkit and its associated plugins) has read/write access to the file, it has access to a database.