> The place for small temporary files. This directory is usually mounted as a tmpfs instance, and should hence not be used for larger files. (Use /var/tmp/ for larger files.) This directory is usually flushed at boot-up. Also, files that are not accessed within a certain time may be automatically deleted.
Trivia: CIS Guidelines (security tasks applied to a server to pass an enhanced security audit to be compliant with a standard, in a soundbite) has an item requiring /var/tmp to be a bind mount to /tmp (as well as setting specific security options on /tmp). A server attempting to pass CIS audits (very common in my work-related experience w/Enterprises) may well not have a unique /var/tmp.
> I thought /var/tmp is for applications while /tmp is for the user.
/tmp is for stuff that is 'absolutely' temporary, in that on many/most systems it is nuked between reboots. /var/tmp is 'relatively' temporary in that applications can put stuff there that they're working on, but if there is a crash, the contents are not deleted and can be recovered across reboots.