"Match play" is a competition format in which the round is played with the goal of winning individual holes. For example, on No. 1, you score 4 and your opponent gets a 5 - you win the hole.
Scoring is kept by comparing the holes won by each player. If each has won the same number of holes, the match is said to be "all square". If you have won 4 holes and your opponent has won 3, you are said to be "1-up" while your foe is "1-down."
Final score reflects the margin of victory and the hole at which the match ended. If the match goes the full 18 holes, the score would be 1-up or 2-up. If it ends before the 18th, the score would look like "3-and-2" (the winner was 3 holes up with only two holes to play, thus ending the match early).
"Halved" is a match play term that means a hole or match was tied. In match play, the goal is to win individual holes, and to win the match by winning the most holes. When a hole is tied - both players in the match score 4s - it said to be "halved," and the players are said to have achieved a "halve." Of course, "halve" is poor grammar (it should be "half," after all), but "halve" is what's used. A match is halved when both players win the same number of holes.
Examples: 1. He's putting to halve the hole. 2. They halved their match.