Your disk space is used by any documents you've saved, any photos or pictures you've saved, spreadsheets you've saved, ..., as well as any email folders you keep under your home directory.
You can stop by the Help Desk and fill out a form to increase your quota setting. Any space you actually use above 600-MB would be charged for a a rate of 1-penny per MB per day. If you had a quota of 700-MB and you were using 650-MB you'd be charged 50-cents per day (for the 50-MB over the 600-MB "free space" value).
Another way to gain some space is to delete things you no longer need to keep around. We have a web page (titled Account Clean Up that provides a semi-automated way to recover some disk space. That will usually be enough to get you enough space to continue working.
One of the biggest consumers of disk space is probably the web browser you use. You may also want to edit its settings on cache files to help conserve disk space. Your browser should also have an option under its configuration settings to clear the cache files.