As mentioned in the comments, their site already explains what the three systems are and what they can be used for.
Arcade Physics is for high-speed AABB collision only.
AABB means axis-aligned bounded rectangles; it means you have objects without rotation, and you're only checking if the image (which is a rectangle) overlaps with another image (so there's a potential collision). This is cheap to compute, and fast, which is probably why they recommend it for high-speed collisions.
One issue with AABB is that it doesn't guarantee that there really is a collision; you may have a completely transparent area overlapping.
Ninja Physics allows for complex tiles and slopes, perfect for level scenery, [...]
Remember how AABB is non-rotated? Ninja Physics will handle rotations (so it can do slopes and complex tiles). This is a more flexible (and probably more accurate) physics model; it's probably slower.
[...] P2.JS is a full-body physics system, with constraints, springs, polygon support and more.
If you need to model springs (eg. something swinging like a pendulum), constraints on forces, and arbitrary polygon shapes (eg. tetrahedron), this sounds like what you want. If you want a frame of reference, think of something like Angry Birds.
Based on your game, you can pick which is the best-fit to your needs. It sounds like a spectrum of speed versus accuracy/complexity (Arcade Physics being the fastest but simplest).