Single means "one" or "individual." When applied to people, it usually means "unmarried." It can be a verb meaning "to call attention to." Sometimes an unmarried person is referred to as "a single." The state of being single is singleness.
Singular is a related word meaning "unique" or "distinctive" or "standing alone in some way." When applied to people, it implies "odd" or "unusual." The noun form is singularity, which is the state of being unique or uncommon. Singular is often used in mathematics and various sciences to describe a property, occurrence, or object that is unique or not related to anything else.