What goes in /var?

That description of /var is self-contradictory. /var contains things that are prone to change, such as websites, temporary files (/var/tmp) and databases. The name is an abbreviation of "variable".

From man hier, which has a "description of the filesystem hierarchy:"

/var This directory contains files which may change in size, such as spool and log files.

/var/account Process accounting logs (optional).

/var/adm This directory is superseded by /var/log and should be a symbolic link to /var/log.

/var/backups Reserved for historical reasons.

/var/cache Data cached for programs.

/var/cache/fonts Locally-generated fonts (optional).

/var/cache/man Locally-formatted man pages (optional).

/var/cache/www WWW proxy or cache data (optional).

/var/cache/<package> Package specific cache data (optional).

/var/catman/cat[1-9] or /var/cache/man/cat[1-9] These directories contain preformatted manual pages according to their man page section. (The use of preformatted manual pages is deprecated.)

/var/crash System crash dumps (optional).

/var/cron Reserved for historical reasons.

/var/games Variable game data (optional).

/var/lib Variable state information for programs.

/var/lib/hwclock State directory for hwclock (optional).

/var/lib/misc Miscellaneous state data.

/var/lib/xdm X display manager variable data (optional).

/var/lib/<editor> Editor backup files and state (optional).

/var/lib/<name> These directories must be used for all distribution packaging support.

/var/lib/<package> State data for packages and subsystems (optional).

/var/lib/<pkgtool> Packaging support files (optional).

/var/local Variable data for /usr/local.

/var/lock Lock files are placed in this directory. The naming convention for device lock files is LCK..<device> where <device> is the device's name in the filesystem. The format used is that of HDU UUCP lock files, that is, lock files contain a PID as a 10-byte ASCII decimal number, followed by a newline character.

/var/log Miscellaneous log files.

/var/opt Variable data for /opt.

/var/mail Users' mailboxes. Replaces /var/spool/mail.

/var/msgs Reserved for historical reasons.

/var/preserve Reserved for historical reasons.

/var/run Run-time variable files, like files holding process identifiers (PIDs) and logged user information (utmp). Files in this directory are usually cleared when the system boots.

/var/spool Spooled (or queued) files for various programs.

/var/spool Spooled (or queued) files for various programs.

/var/spool/at Spooled jobs for at(1).

/var/spool/cron Spooled jobs for cron(8).

/var/spool/lpd Spooled files for printing (optional).

/var/spool/lpd/printer Spools for a specific printer (optional).

/var/spool/mail Replaced by /var/mail.

/var/spool/mqueue Queued outgoing mail (optional).

/var/spool/news Spool directory for news (optional).

/var/spool/rwho Spooled files for rwhod(8) (optional).

/var/spool/smail Spooled files for the smail(1) mail delivery program.

/var/spool/uucp Spooled files for uucp(1) (optional).

/var/tmp Like /tmp, this directory holds temporary files stored for an unspecified duration.

/var/yp Database files for NIS, formerly known as the Sun Yellow Pages (YP).