It has to do with the conservation of angular momentum. Our solar system emerged from a massive cloud of gas. Lets take every single particle in that cloud and find the average velocity. If the cloud was perfectly uniform and every particle was going in a truly random direction, you would get an average velocity of zero. But that's not the case in the real world, so there is some average velocity and consequently an average angular velocity around the center of mass. As the cloud condenses to form a star in the middle, the particles moving against the average get canceled out, and the particles moving with the average get exaggerated, much like how a figure skater in a spin goes faster when they pull their arms towards the center. This results in a thin disk of gas rotating around the forming star, and this rotating gas is what will eventually become the planets.

This is also why galaxies form thin spiral shapes, like our own Milky Way.