The Earth and the other planets in our solar system spin because the solar nebula that they formed from was also spinning. A solar nebula is basically a big ball of cosmic dust that spins and flattens into a pancake-shape. Gravitational attraction between dust particles causes them to form bigger and bigger particles. Eventually the particles grow into planetesimals (tiny planets) and planets. The reason that the planets spin, just like the original pancake of cosmic dust was spinning, is because of a law of physics called the conservation of angular momentum.

This law basically says that once something is spinning, it must continue to spin (forever if nothing interferes). Because the original nebula was spinning, the Earth and all of the other planets spin as well.

Why they nebula and bigger things, like galaxies, were spinning in the first place is a more difficult question. I don’t know the answer to that, but I think that it probably relates to the big bang, when the universe started. You can probably find more information about this interesting topic on the NASA website (nasa.gov).