What keeps the planets of the solar system moving in their fixed orbits? Models of the solar system show each planet moving around on its own orbit.

Is is really because of the Sun that every planets remains in its own fixed orbit?
It is ,of course, gravity which keeps the planets circling the sun. They are actually falling toward the sun, but as the sun is a sphere, its surface keeps curving away, so they never get any closer to it. Because they are in a state of free fall, they are in effect weightless with respect to the sun, just as the space station is weightless with respect to the Earth, and as they use no energy in falling they can do it for ever. If you are wondering why you don't feel weightless, that's because of the gravitational field of the Earth. If the space station was a massive body like the moon.the astronauts wouldn't be weightless,but although the space station has a gravitational field of its own it is so trivial that it has no measurable effect on the astronauts.