Pillage is the mode a match enters once a player has only one unit remaining and while the other player has at least 2 or more.
Pillage mode begins when the first player loses all-but-one of his/her units. Once in Pillage, the player with more than one unit is allowed to move his/her units successively after the player with remaining unit moves. Pillage lasts as long as one player has at least 2 or more units remaining.
You can take advantage of this mode to level up your player of choice by letting then have the final kill shot.
Example: Player 1: 3 units (A,B,C) versus Player 2: 2 units (X,Y)
Normal Turn Sequence: A -> X -> B -> Y -> C -> X -> A -> Y ->...
Pillage Turn Sequence (Player 1 kills unit Y on unit A's turn): A -> X -> B -> C -> A -> X ->...