Internal force and centre of mass

I have still not yet learn about the centre of mass of a system but I really do need to solve this question that keeps bugging me. I know that internal forces cannot accelerate the centre of mass of a system, but assuming that I have a block-earth system and the block is dropping from a point and considering that gravitational force is an internal force for this system, won't the centre of mass accelerate since the block is accelerating while the earth is not?

Btw, it would be great if someone can explain the concept of centre of mass of a system to me in a much simple way.

Thanks

Actually, from Newton's Third Law of motion, the Earth is attracted towards the block with exactly the same magnitude of force, with which it attracts the block. But we don't see it accelerating simply because its mass is (numerically) much, much greater than the gravitational force. You can also calculate this acceleration, from Newton's law of universal gravitation. We have: $$F=\frac {GMm}{R^2}$$ Hence, $$a_{Earth}=\frac {F}{M}$$ which comes out to be negligibly small in most cases, hence unnoticeable.