Mainly because there’s no air in space to slow them down [1].
Think about swinging a ball at the end of a string, around and around. The ball “wants” to go flying away in a straight line, but goes in a circle because you keep diverting its course by pulling on the string.
Gravity does the same kind of thing. It pulls satellites (and the moon) in circles around the Earth. And the Earth around the Sun.
You need the right starting conditions (position, speed and direction) to get a circular orbit though. It’s also possible to get an elliptical (oval-shaped) orbit, where you fall gaining speed toward a low point (perigee), then climb losing speed toward a high point (apogee). Most satellite orbits are circular, except for maybe a few science missions.
[1] Not strictly true, there’s a tiny bit of air at typical satellite altitudes, but it takes years / decades / centuries to add up enough to make a satellite fall out of the sky.
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