When a fruit falls on the earth from a tree, why doesn't the Moon fall on Earth?

The fruit is not traveling horizontally at orbital speed.

Instead of fruit, let’s play with a cannon ball.

If you drop a cannon ball, it falls on your foot, but if you fire it out of a cannon, it flies for a certain distance before gravity draws it down to the ground. The more power you put in the cannon, the faster the cannon ball will fly, so the farther it will fly before hitting the ground.

Now, imagine you have a magical cannon that can fire a cannon ball arbitrarily fast without blowing itself up, and imagine you can fire this cannon from the summit of Mt. Everest so no mountains or structures get in the way.

Now imagine you fire the cannon over and over again, each time increasing the power charge. At first, the cannon ball just flies farther and farther as the charge is increased. But pretty soon, it’s traveling out over the horizon—the surface of the Earth is curving out from under it as it flies. If you keep increasing the speed, eventually there comes a point where the Earth is curving away at the same rate to ball is traveling, so the ball just goes round and round in a circle.

And that’s what an orbit is. When an object is flying away as the same rate gravity is causing it to fall, it circles in orbit.

That’s why the moon doesn’t fall to Earth. It is falling, right now, but it’s the world’s biggest cannonball, and it’s drifting off on a tangent as the same rate it’s falling, so it goes around and around in its orbit.