In Asteroids: Outpost, asteroids are continually raining down in small numbers, but a countdown at the top middle of your screen will indicate when larger Asteroid showers will happen.
Asteroids will damage your base if they land on it. Also, a certain percentage of them are full of ore. To protect your Base or to release the ore rocks from the Asteroids, you'll need to shoot them down, and that requires a Big Turret.
In the future, Asteroids from an Asteroid Shower (which will eventually be balanced to hold more valuable and rare items) will be outlined in white. When you shoot a white-outlined Asteroid, a certain percentage of them will break into smaller, ore-filled Asteroids which will land on the ground and can be mined.