An assignment is a job that someone has been told to do, usually by an employer or a teacher.
1. John had an assignment as a photographer.
2. This was a straightforward public-relations job, an easy assignment for beginners.
3. She hastily set them another assignment before letting the class go.
An assignation is a secret meeting, usually between lovers. Assignation is an old-fashioned word.
4. The couple had made the assignation on the beach.