Strictly speaking, everything is moving. Motionlessness is impossible, because there’s no objective motionless state. Stopping completely is just as impossible as breaking the speed of light.
More to the point, though; the Sun is moving because the gas cloud it was formed from was moving in (roughly) the same direction, and it keeps moving because there’s nothing to stop it or slow it down. The only real force is the pull of the gravity of the Milky Way, continually pulling it in orbit around the core.
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