ERA estimators are used to predict future ERA based on events that are most controlled by the pitcher. They remove the defense and luck of sequencing and only focus on these pitcher controlled events.
For example, Fielding Independent Pitching (FIP) is based on strikeouts, walks, hit by pitches, and home runs. If a pitcher continues at these current rates, one would expect his ERA to match his FIP in the future (or at least come close to matching it).
Skill-Interactive Earned Run Average (SIERA) is a more complicated ERA estimator that uses batted ball events to predict future ERA.