A quick definition of degree of kin:

The degree of kin is a way to measure how closely related two people are in a family. It helps determine who inherits when someone dies without a will. To figure out the degree of kinship, you count how many steps there are between the two people in the family tree. The closer the relationship, the lower the degree of kin. For example, a cousin is in the fourth degree of kinship. The law also uses degrees of kinship to decide who can get married. Some relationships, like siblings, are too close and are not allowed to marry. Finally, a degree can also refer to a title given to someone who has completed their studies at a school or university.