Someone who is on assignment is doing a particular job or piece of work, usually in a particular place where they have been sent for a period of time.

Both journalists were killed while on assignment in the region.

He was on assignment for the New Yorker, where he was a photographer.

Her husband, a helicopter pilot, had been on assignment in Iraq for over seven months.

She told people she was in the area on assignment.

He was suffering from a disease he contracted while on assignment in Panama.