To sit down (often temporarily); to take a seat on something like a chair or bench.
どうぞ腰掛けてください。
Please have a seat.
公園のベンチに腰掛けて本を読んだ。
I sat on a park bench and read a book.
台に腰掛けて作業を続けた。
I perched on the counter and continued working.