what types of files are you deleting? to see how large a file is, click on its icon in the Finder once (so it's highlighted), and then go to File and click on Get Info (or hit command and i keys together).
if you are just deleting things like Word docs, you aren't going to make much of a dent...
when was the last time you restarted, by the way? restarting can get rid of some temporary files, some of which can grow rather large.
as to your question, the user "drive" is probably just your user (also called Home) folder. it's a folder that's on your hard drive. if you click on the Macintosh HD icon on the desktop, you should see some folders, like Applications and Users. if you click on Users you should open it up and see your username under a house icon. this is your user folder (user "drive"?)