Access Point mode is when you want to connect the router up to an Internet source via cable. This differs from the default method of connecting to the Internet; while the default method plugs directly into the Internet, using Access Point mode allows you to connect it via cable to, perhaps, another router.
Using Access Point mode is ideal if you want to extend the WiFi range, but the router you’re using to extend it isn’t too far away from the main central router. The cable will ensure you get the best possible speeds between the access point and the central hub, and you don’t have to worry about anything interfering with a WiFi signal.
This is a great choice if you want to extend your home connection past something like a solid wall that’s blocking WiFi connections. Simply connect the router to the central hub, place it on the other side of the wall, and put it in access point mode.