It's angular momentum. The rotation starts when gravity begins pulling objects together. They have different masses and speeds so eventually they collapse into a sphere like a planet or star. These initial energies combine into a single moving object, which eventually goes from erratic chaotic rotations to one unified rotation over time.

Then anything of lesser mass will be pulled into the plane of rotation. So everything in the solar system eventually aligns to the same flat plane thanks to the sun's mass and rotation.

Same thing happens at larger scales, where galaxies are roughly flat.

Keep in mind that nebulae and elliptical galaxies exist as well. Under different circumstances things don't always turn out so flat.