Imagine a stretched rubber sheet. If you place a heavy ball in the center of the sheet, it will cause the sheet to dip. If you then place a smaller ball near the heavy ball, it will roll down the dip and eventually collide with the heavy ball. This is because the curvature of the sheet causes the smaller ball to move towards the heavy ball.
In the same way, the curvature of spacetime caused by the presence of a massive object, such as a planet or star, causes other objects to move towards it. This is what we experience as gravity.
The greater the mass of an object, the greater the curvature of spacetime it creates, and the stronger the gravitational force it exerts. This is why objects fall towards the Earth with a greater acceleration than they fall towards the Moon.
Gravity is one of the four fundamental forces of nature. The other three are electromagnetism, the strong nuclear force, and the weak nuclear force.