The idea is simple. In normal combat, turn order is always clock-wise.
If you're in the fourth slot in your team, you always are fourth to have your turn.
Turn priority changes this. Turn priority on your team goes clockwise, then all non-priority turns go in clockwise order.
This allows someone in fourth slot to use a wand hit to remove a Tower Shield, for example. Also, this could open the door for minions with priority wand hit attacks, or priority blades, or priority traps.
The intention with this mechanic is to allow minions to become a much more useful, less-frequently overlooked game mechanic.
Please add this to the next test realm for a more minion-focused school, such as Myth or Death. :) I'd love to see how this could affect PvE and PvP.