For the anim BP, this is how I see the relationship. The animation BP tells how to do stuff based on State, like in UE4. Like if he is Jumping how high before you change from the start Jumping to the apex, then to the landing.
Animation Layers describe how you move from one state to another by blending the current state with other animations to get the desired result(Running and shooting overhead)
The Character BP is just to say WHICH animation to use for the other two. When running(Anim_BP) use this animation(Character BP), how you should combine the animations, Shooting when jumping(Anim Layers). Hope I got this right, but that is how I think they are working.