to say that you have arrived and sign an official book when you get to a hotel, etc.

After booking into our hotel, we went straight down to the beach. 登记入住酒店后，我们就径直去了海滩。

As soon as she arrived in Tokyo, she booked in at her hotel. 她一到东京就登记入住了酒店。

to arrange for someone or for yourself to stay at a hotel, etc.

They've booked us into the hotel in the main square. 他们已经安排我们入住主广场的酒店。

I've booked you in at the Savoy. 我已经安排你入住萨伏伊旅馆。

I drove up there and booked myself in at a hotel down the road.