One Rep Maximum (or 1RM) is an estimate of your best possible single rep lift for an exercise. We use it because it's helpful as a single number to use when comparing different sets from a workout. Many popular workout programs are based on a percentage of your 1RM as you progress, rather than giving specific weights to use.
We use the Brzycki formula. It can break down at higher rep numbers, but we found it's generally very representative.