Imagine a golfer who is very consistent except for one terrible hole per round. He makes no worse than bogey for 17 holes, but one hole he blows up with a 12. Ouch! That 12 doesn't really reflect the golfer's potential, yet that 12 - if counted for handicap purposes - would impact the golfer's handicap index.
The purpose of ESC is to minimize the effects of such "disaster holes." ESC does this by setting a limit to the score a golfer can turn in on any given hole, based on that golfer's course handicap. A golfer with a course handicap of 8, as an example, has a maximum per-hole score of double bogey when ESC is in use.
Golf courses should have available a chart that shows golfers what the ESC maximums are based on course handicaps. That chart is also available as part of our FAQ, "What is Equitable Stroke Control?" See that page for further explanation of ESC and for the per-hole maximums.
But also note that ESC applies only to golfers who use the USGA Handicap System and are playing rounds that will be turned in for handicap purposes. And even those golfers still count all their strokes. If you use 95 strokes, then your score is 95. But when you turn in that score as part of your handicap, you apply ESC and that resulting total is what is submitted to the handicap committee.