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/var is a section, normally a seperate partition, to store "variable" and always changing files. Such as Log Files, your Web Server, FTP server files, etc.
If the /var partition is nearly maxed out, just delete some of the files. (just stay away from /var/log)
In console, SU (Super User), just type 'rm filename' for files.
If you want to remove directories, 'rm -f-R foldername', where -f is to force the deletion, and -R is to recurse through all files/directories inside the folder you want to delete.