A relationship between two people is created when two separate identities (see Who Am I?) interact and create a shared reality (see Properties of Reality) between them. The relationship is that shared reality.
Relationships can be formed within the physical world (two people went to the same high school) and they can be formed within the mental world as well (blue is related to a blue window, a blue house, and a little blue corvette).
People exist both in the physical world (bodies, possessions) and in the mental world (thoughts, likes and dislikes), so in order to fully describe and understand a relationship between two people we must look at the physical and mental relationships together as one. The relationship between people is further complicated because people also have emotions which do not follow logic. They are limited by their Judgment and Logic (see What is Judgment and Logic).