Triperspectivalism is basically looking at things from three, hence the "Tri" like in "Tri-angle", perspectives or views. When we typically approach a subject, a person, or ideas we have one perspective based on our history, our own views, or experience. However, as we all know, it's helpful to approach objects from different angles to get a complete view. This three-viewed approach is a good starting point to help us consider multiple views, or angles, from which a topic or situation can be evaluated. Since there are three perspectives, or views, graphically this type of approach can be represented with triangles.
This prophet, priest, and king structure is the theological basis for our form of Presbyterian government made of shared leadership between teaching elders, also called pastors, (prophet), ruling elders (king), and deacons (priest).
This three pronged approach to viewing ideas isn't limited to theology. How should I consider raising my children? Normatively I should be concerned about their physical health and well being, situationally I should consider how they will function emotionally and socially in the world, and existentially I should consider their spiritual health. How about hiring someone? Normatively do they meet the requirements for this job, situationally how will they preform, and existentially what is the spiritual and personal dimension? What should my life group do? Normatively we should study the bible or do other studies, but situationally how are we affecting the world, are we going out in any way, and then existentially are we collectively praying for each other, doing soul care and fellowshipping?
I hope this makes sense and can help you as it has helped me take multiple perspectives on circumstances and decisions. At the very least it will help you consider things not only from a material perspective but a spiritual one as well. I'd be excited for any other triangles you might come up with! You can click here to see an example of how a triperspectival approach to the gospel helps give a fuller view of the gospel.