Interesting and neat trick from systemd
/run/user/$uid is created by pam_systemd and used for storing files used by running processes for that user. These might be things such as your keyring daemon, pulseaudio, etc.
Prior to systemd, these applications typically stored their files in /tmp. They couldn’t use a location in /home/$user as home directories are often mounted over network filesystems, and these files should not be shared among hosts. /tmp was the only location specified by the FHS which is local, and writable by all users.
However storing all these files in /tmp is problematic as /tmp is writable by everyone, and while you can change the ownership & mode on the files being created, it’s more difficult to work with.
So systemd came along and created /run/user/$uid. This directory is local to the system and only accessible by the target user. So applications looking to store their files locally no longer have to worry about access control.
It also keeps things nice and organized. When a user logs out, and no active sessions remain, pam_systemd will wipe the /run/user/$uid directory out. With various files scattered around /tmp, you couldn’t do this.