By the leaving-home function SEAT refers to activation of parts of the lighting system on the car as soon as the central locking is opened via the remote control. These include dipped beam, tail lights and number plate lights. This is intended to assist the driver who wants to get into the car (ie: who is figuratively leaving home) and facilitate finding his way to the car in the dark.
In reverse, it is the same with the coming-home function, when after locking via the remote control, the lighting of the car is left switched on for some time before it automatically shuts down.