The /var contains data that is changed when the system is running normally. It is specific for each system, i.e., not shared over the network with other computers.
A cache for man pages that are formatted on demand. The source for manual pages is usually stored in /usr/share/man/man?/ (where ? is the manual section. See the manual page for man in section 7); some manual pages might come with a pre-formatted version, which might be stored in /usr/share/man/cat*. Other manual pages need to be formatted when they are first viewed; the formatted version is then stored in /var/cache/man so that the next person to view the same page won't have to wait for it to be formatted.
Any variable data belonging to games in /usr should be placed here. This is in case /usr is mounted read only.
Files that change while the system is running normally.
Variable data for programs that are installed in /usr/local (i.e., programs that have been installed by the system administrator). Note that even locally installed programs should use the other /var directories if they are appropriate, e.g., /var/lock.
Lock files. Many programs follow a convention to create a lock file in /var/lock to indicate that they are using a particular device or file. Other programs will notice the lock file and won't attempt to use the device or file.
Log files from various programs, especially login (/var/log/wtmp, which logs all logins and logouts into the system) and syslog (/var/log/messages, where all kernel and system program message are usually stored). Files in /var/log can often grow indefinitely, and may require cleaning at regular intervals.
This is the FHS approved location for user mailbox files. Depending on how far your distribution has gone towards FHS compliance, these files may still be held in /var/spool/mail.
Files that contain information about the system that is valid until the system is next booted. For example, /var/run/utmp contains information about people currently logged in.
Directories for news, printer queues, and other queued work. Each different spool has its own subdirectory below /var/spool, e.g., the news spool is in /var/spool/news. Note that some installations which are not fully compliant with the latest version of the FHS may have user mailboxes under /var/spool/mail.
Temporary files that are large or that need to exist for a longer time than what is allowed for /tmp. (Although the system administrator might not allow very old files in /var/tmp either.)