A transitive verb meaning to give someone lodging or shelter (to put someone up). The corresponding intransitive verb is 泊まる.
今夜はうちに泊めてあげるよ。
You can stay at my place tonight.
出張中、会社がホテルに泊めてくれた。
While on the business trip, the company put me up at a hotel.
遠くから来た友達を実家に泊めた。
I put up a friend who came from far away at my parents' house.
嵐で帰れない人をボランティアが避難所に泊めた。
Volunteers sheltered people who couldn't go home because of the storm.