An assignation is a secret meeting. You might have an assignation with your new girlfriend if the two of you were keeping your relationship private.
Any kind of clandestine meeting can be called an assignation, but it most often describes a romantic tryst. Every encounter between the two main characters in Shakespeare's "Romeo and Juliet" is an assignation, since their families don't approve of their relationship. The word assignation meant "appointment by authority" in the 14th century, from the Latin assignationem, "an assigning or allotment," with the "meeting by arrangement" meaning arising in the late 17th century.