While tying her shoes he says "You don't remember me, but I remember you". In this beautiful love story this couple are in old age and she is battling Alzheimer's. However, he doesn't really look at caring for her as a job, but a reflection of the memories shared and how he knows how to make her happy.
When they start dancing at the end, a full life reflection occurs and he realizes they can still share their love no matter what.