HELP: File system full

I tried to change a password for a user. After I put the new password in and hit enter, I got error:

/: write fail, file system is full
password: failure rebuilding password entry, contact your system administrator.
apr. 11 … idea kernel: uid0 on /: file system full

Note: I has been doing manually backup on tape on /var, /usr, /usr/home. My boss told me to used command: gtar czvf /dev/nrst0 /var

In general speaking, I am backing up on tape.
I could see the light on soon as I enter command. Why the file system filled up?

Any quick solution, any Expert?

Thanks