"On assignment" typically refers to a task or job that a person has been assigned to accomplish. Synonyms for "on assignment" include "on duty," "on task," "on the job," "on a mission," "engaged in a project," "assigned to a task," "working on an assignment," "deployed on a mission," and "in the field." Each of these phrases conveys the same general idea of a person actively carrying out a designated assignment. The words chosen may vary depending on the context in which the phrase is being used, but they all serve to emphasize the importance and seriousness of the task at hand.