Arena matchmaking works by matching up players with similar flock power. Since it's not always possible to match players with exactly the same flock power, sometimes your opponent may have slightly higher or lower flock power than yourself. However, the battles are designed to always be fair!
The battles don't occur in real-time, but instead you play against another player's performance in the same level from an earlier time. Although it isn't a live battle, the cards played and scores earned are still really from another player. Good luck!