Describes a family member with whom the reference person does NOT have a "blood relationship" such as direct or shared descent. Could be used to describe a relationship created by marriage or by adoption.
The definition of family has never been fixed and continues to evolve. Nevertheless, most cultures in most times have afforded a special status to relationships arising through birth. Relationships involving descent from a common ancestor (that is a shared genetic heritage) are still commonly called "blood relationships".
Any family relationship that does not meet the criterion of direct or of shared descent can be described colloquially as a "non-blood" relationship. So a person who joins a family by marriage or adoption could be described as a non-blood relative of those born into the family.
For example, the spouse of your parent's sibling is a member of your family but not a blood relative.
If you need to find the English-language term for the relationship between two members of a simple or complex family, the Steve Morse relationship calculator will help.