Syslog Facility is one information field associated with a syslog message. It is defined by the Syslog protocol. It is meant to provide a very rough clue from what part of a system the message originated from. Tradidionally, under UNIX, there are facilities like KERN (the OS kernel itself), LPD (the line printer daemon) and so on. There are also the LOCAL_0 to LOCAL_7 facilities, which were traditionally reserved for administrator and application use.
However, with the wide adaption of the syslog protocol, the facility field contents has become a little less clear. Most syslog enabled devices nowadays allow configuring any value as the facility. So it is basically left to distinguish different classes of syslog messages.
The facility can be very helpful to define rules that split messages for example to different log files based on the facility level.