Precipitation is rain, snow, sleet, or hail — any kind of weather condition where something's falling from the sky.
Precipitation has to do with things falling down, and not just from the sky. It's also what happens in chemical reactions when a solid settles to the bottom of a solution. If you have hard water where you live, you might find lime deposits — a flaky white crust — on your faucets and showerhead. That's caused by precipitation of the minerals in the water. The minerals settle out — they precipitate — and clog the pipes.