The Baseline Execution Index is a metric added to the US military concepts of Earned Value. It is sometimes referred to as the military efficiency scale. The formula is:
BEI = Tasks with Actual Finish Date / (# of Baseline Tasks Scheduled to Finish Prior to Status Date +Tasks Missing Baseline Start or Finish Date)
In simple terms, its a ratio of the number of tasks that finished in a period to the number of tasks that were supposed to finish in a period. Hence the name as it is checking against performance of the project baseline.