Question

if you push a block of wood under the water, you feel a force on your hand. why?

Answer 1

Newton's third law of motion. When you push a body, that body pushes you back with the same amount of force.
Also, it's not only with wood under water, you can do it pushing a wall (Or any other object, for that matter), you'll feel a force that is the same as if the wall was pushing you.

Answer 2

Well, its because of Newton's third law that is every action has an equal and opposite reaction. But its just one way of saying it. Here force applied by you is not equal to the force applied by water on the body, if the body is in motion and is going inwards.
I hope you know about Buoyant force that is exerted by the liquid whenever a body is emerged in fluid. Its is simply as result of pressure difference inside fluid.
so from this pressure diff is dg(h2 - h1) in upward direction and so force on the body is dg(h2 - h1) A in upward direction and this upthrust is felt by us.