Any plate or plate program (license plate or dinner plate) that you have an affinity for or a strong liking for or attraction to someone or something.
The Royal Family is announcing the release of a new Affinity Plate this year commemorating the passing of someone important and obviously Royal and to whom they had an affinity for.
or,
Some license plate program that ensures that Google will get a lot of traffic from people who have no idea what affinity plates mean.