This is a really cool question that lets me post one of my favourite videos!
The current prevailing theory is that matter can bend space. The more matter you have, the more space will bend. So a huge mass like the sun bends space a lot. Smaller celestial bodies like the planets do the same thing, but by a smaller amount. This results in “gravity wells”. A smaller celestial body orbits a bigger one when it gets caught by the larger body’s gravitational pull.
So the sun has a huge gravitational pull which attracts all the planets in our solar system. Each planet has a pretty big gravitational pull which keeps things like moons in orbit.
A great visualization that teachers use to explain this is to stretch a latex sheet across a hula-hoop and then drop large masses on it to show how “space” bends:
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