In the context of multiuser computer systems, hard quota is the amount of storage space that the user absolutely can not exceed. Write operations that would exceed the hard quota limit simply fail.
If you find yourself having reached the hard quota limit, you should delete something. Look for unused files, installation logs, Netscape cache directories and core files.
Be aware that compressing stuff may not work; most compression programs first write the compressed file and afterwards delete the original files. Failure to write the compressed file may result in inconvenience or complete disaster.
See also: soft quota, quota and quota policy.