A somewhat formal or bureaucratic term for a person who works at a company or organization. Often used in official contexts.
He is an employee of the city hall.
Improve the welfare benefits of the employees.
職員 also means staff or personnel, but is broader and can refer to members of an organization. 勤務員 emphasizes the act of working (勤務) at a place.
Compound of 勤務 (kinmu, 'work, service') + 員 (in, 'member, person'). The word is a straightforward Sino-Japanese formation.