Henry goes to his father's apartment to ask him for his mother's rings because he wants to give them to Clare when he proposes marriage. He runs into Mrs. Kim. When he tells her about Clare and that he has come to get his mother's rings, Mrs. Kim reveals that his father is not doing too well anymore. He's been letting himself and his place go, and hasn't been paying rent.
Henry finds his dad in a deplorable state. His alcohol addiction has robbed him of his ability to play the cello. When Henry tells him he's getting married, his father responds, "Who would marry you?" (1.10.80). Henry describes Clare and then asks him for the wedding and engagement rings. He adds that he thinks his mother would have wanted Clare to have them and that he's been time traveling to see his mother many times. He mentions to his father that, as a young couple, the two looked so happy, and he wishes he could have met his father then. His father warms up and gives him the rings.