This console message indicates that an NFS-mounted partition has filled up and cannot accept writing of new data. Unfortunately, software that attempts to overwrite existing files will usually zero-out all data in these files. This is particularly destructive on NFS-mounted /home partitions.
Find the user or process that is filling up the file system, and stop the out-of-control process as soon as you can. Then delete files as necessary to create more space on the file system (large core(4) files are good candidates for deletion). Have users write any modified files to local disk if possible. If this error occurs often, redistribute directories to ease the demand on this partition.
For more information on disk usage, see the System Administration Guide, Volume 2. If you are using AnswerBook online documentation, "managing disk use" is a good search string.