The Trinity of Magic is a triangle much like the Weapon triangle. It contains Anima Magic, Light Magic, and Dark Magic with Anima Magic besting Light Magic, Light Magic trumping Dark Magic, and finally Dark Magic beating Anima Magic. A second triangle is formed by the three different types of Anima magic: Wind is strong against Thunder, Thunder is strong against Fire and Fire is strong against Wind. In Fire Emblem: Genealogy of the Holy War, both Light and Dark were strong against Anima, while being neutral to each other. Like the weapon triangle, an advantage can make impossibilities for the opponent to damage, critical, or hit you.
Path of Radiance lacks Dark magic and only contains the Anima magic triangle, ultimately leaving Light magic as neutral. In this triangle, Fire beats Wind, Wind beats Thunder, and Thunder beats Fire.
In Radiant Dawn, Dark magic returns, and there are now two Trinities of Magic: the familiar Anima-Light-Dark triangle and the Fire-Wind-Thunder triangle.