When two high powered spells of two elemental runes are cast at the same time they have a chance to unite and form a united magic attack. United Magic attacks are far stronger then only single rune spell could ever be. Almost every game with a United Magic opinion requires that the final spell of both runes be cast in order to work.
Ex. Rage's Final Flame and Thunder's Thunder Storm to create Flame Array
The only game that this isn't required is Suikoden V but the both spells must still be of the same level. Also the weaker the level the weaker the spell.
Unite Magic. Unite Magic is a lot harder to pull off in I and II because it only occurs if you use two level 4 magics from corresponding runes (either from child or parent runes) in the same round. In III, IV and V, the game auto-detects these Unite Magics so you can select them before your turn without stumbling upon them. The character with higher Speed will add his or her Magic stat to the spell. Targeting specific enemies is tricky with one particular Unite Magic, Thor (it is the only single-target Unite Magic). The person who is faster and has the Lightning/Thunder Rune can direct the magic at a specific enemy, otherwise it chooses the first enemy on the list.
Unite Magic is incredibly powerful, and is the only way to match the Soul Eater's Judgment spell in damage potential normally (outside of Unites).