to be expecting someone or something and be prepared to deal with him, her, or it

When the thieves left the building, the police were waiting for them. 当盗贼们离开那栋楼的时候，警察正在等着抓他们。

If something is waiting for you, it has been left or prepared for you to collect, use, enjoy, or deal with when you arrive.

An envelope was waiting for me when I got home. 我到家时看到有我的一封信。

Uma had a cup of coffee waiting for me, along with a plate of biscuits. 乌马泡了一杯茶等我喝，还准备了一盘饼干。

to delay serving a meal until someone arrives

Don't wait dinner for me - I'll be home late. 别等我吃饭了——我会很晚才回家。