This is a very important distinction, because AA goes to great lengths to clarify that the "higher power" is one of your own understanding. It is not Jesus, it is not a Christian-Jewish-Muslim God. It is simply something "bigger than yourself" which exists and which you can feel comfortable addressing.
It could be the Pacific Ocean for all you care. It just must be bigger than you.
If you're not religious, community can be your higher power. The point is more that will-power alone is not enough for some people.
This is why addicts talk to other addicts; because other addicts "get it" and can provide help in overcoming the problem that isn't just "learn how to use your own will power". That's just condescending.
It's obvious, really; if it were that simple, there would be a great deal less addicts in the world.