To expel or drive someone/something out; to force someone to leave a place.
部屋に入ってきた猫を追い出した。
I chased the cat that came into the room out.
彼は飲み会で酔っ払いを店から追い出した。
He kicked a drunk out of the bar at the drinking party.
家賃を払わないので大家に追い出された。
He was evicted by the landlord for not paying rent.