The basic issue

Gravity holds us to the Earth and makes apples drop to the ground when they fall off a tree. It controls how the Moon moves round the Earth and how the Moon causes tides on Earth. It controls how the Earth moves round the Sun and how the Sun moves round the Galaxy. But it’s not a force. That was Einstein’s great discovery. How can we say that? Well because you can, at least for a while, simply make it vanish! How do you do that? Just let go! In other words, jump off a building, and you’ll feel no gravity as you fall down (hitting the Earth does not count as falling down). More gently, join a freely orbiting space station crew, and you’ll find life difficult because there will be no felt gravity to hold you down on your seat or to hold your coffee in a cup. In short, what appears to be a gravitational force actually depends, locally at least, on how you are moving. You can make it go away by allowing yourself to fall freely.

The reason why

The reason this is true is because the gravitational mass of a body is the same as its inertial mass. This is what Galileo discovered, allegedly, by dropping objects of different weight from the Leaning Tower of Pisa (that experiment has since been done much more accurately by modern physicists - see this video for a feather and a ball falling at the same speed). That means that if you are in lift and the rope breaks, you and everything around you will fall at the same rate as the lift – so you will no longer feel gravity holding you to the floor of the lift.  This was Einstein’s “happiest discovery”.