Moons orbit a planet as they feel a gravitational attraction to the planets mass. Moons can be formed in several ways, they could be captured objects that passing close to a planet become trapped by the gravitational attraction, however, I believe the most likely process is from dust clouds of matter close to planets that form moon by gravitational collapse in the same way as the planets are formed. While the Earths moon is believed to have been formed by another planet smaller than the Earth that collided with the Earth, throwing matter out into space which then accumulated together due to the gravitational force to form the moon.
It’s the same reason star have planets.
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There is a lot of small stuff around at the beginning of a solar system’s life. Slowly it coalesces (clumps together because of gravity) into small planetoids (mini planets). As these mini planets hoover up all the rest of the small rocks left over, some get really big (these become the planets) and they end up either capturing some of the smaller planetoids into their own orbits (these have become the big one’s moons).
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Sometimes planetoids collide, like in the case of how the Earth got it’s Moon. The video link below shows a simulation of the collision that made our moon.
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