Combo Priest is an archetype that usually revolves around Divine Spirit and Inner Fire to burst down the opponent from high health totals.The deck has many variants, but the core gameplan of the deck remains the same - use Divine Spirit and Inner Fire on a minion with high health to finish out the game.
With the release of Saviors of Uldum, Priest got some really good cards that can fit into the Combo Priest archetype in the form of High Priest Amet, Holy Ripple, Injured Tol'vir, and Psychopomp. These cards have improved the overall consistency of the archetype.
The aggressive variant makes use of Lightwarden as an early game threat. Lightwarden in Combo Priest is capable of closing out games without requiring Divine Spirit and Inner Fire which is a huge plus in specific matchups.
The deck's gameplan is to draw a lot of cards, generate strong board pressure, and burst down opponent with Divine Spirit and Inner Fire. The potential to close out games as early as turn 5 makes it a scary deck to face.