Quartering is when you win only a quarter of a pot in a high/low game. Conversely, being quartered is winning all of the high (or low) and chopping the low (or high). For example, if you lose the high, and tie for low, you have quartered your opponent.
Consider: Your opponent holds: JT45 rainbow
You hold: A5K4 rainbow
The board comes: A K Q 2 3
You lose the high (your AAKKQ vs opponent's AKQJT) and split the low (A2345 vs A2345).