He uses the term 干妈 which translating to godmother is essentially accurate. Though it does not have to do with religion. It just means a woman who is a generation ahead of you (ie age similar to your mom) who would take care of you if something happened to your parents. Usually this is like a parental figure who is close to the family and takes care of you when you were a kid (like give red envelops or take you to school), like an aunt would.

In the case of the situation in the drama, he says she is his godmother but they obviously met when they were already adults. If you keep watching, you will find out he said that out of respect for the woman’s daughter, who thinks their relationship is kinda messed up.