Way earth is moving?

It's not! Earth is rotating, and you're on the Earth. So you are the one who's moving! The Earth rotates around it's axis. It turns because of its formation. It rotates 24 hours that is one day. When the Earth turns, it causes day and night. It rotates counterclockwise. Hence, don't say the Earth is moving. Say the Earth is rotating or even revolving.

The earth is moving (spinning and moving on its orbit around the Sun) because it inherited the movement from the Solar System, which itself inherited the movement from before. Basically, it continues to spin because of inertia (tendency to remain unchanged), and it preserves the movement of matter from before it was formed.