To sit down; to take a seat (to rest one's hips on something). A common, everyday expression.
ベンチに腰を掛けて、しばらく景色を眺めた。
I sat down on the bench and looked at the view for a while.
どうぞ腰をかけてください。すぐ始めます。
Please have a seat. We'll start shortly.
疲れたので、階段の手すりに腰を掛けて休んだ。
I was tired, so I rested by sitting on the stair railing.
彼は来客用の椅子に腰を掛け、話を聞いた。
He sat down in the guest chair and listened.