If by "fixed" you mean stationary then the sun is not fixed. It is in orbit around the centre of the Milky Way, travelling at a speed of around $250$ km/s relative to the centre of the Milky Way. At this speed it travels one astronomical unit (the average distance between the earth and the sun) every seven days, and travels one light-year in about $1,190$ years. In other words, its speed relative to the centre of the Milky Way is about $0.1 \%$ of the speed of light.
The sun appears to be fixed relative to the background stars (once you take into account the earth's orbital motion around the Sun) because the stars are very far away, and also because most of the stars visible to the naked eye are also orbiting around the centre of the Milky Way in orbits that are very similar to the sun's orbit.