What is "strokes gained" in golf?
Strokes gained is a method of measuring a golfer's performance that revolutionized how people think about golf strategy and how they compare the performance of golfers.  

Simply put, strokes gained measures how many strokes a player gains on every shot they hit in a round of golf.  

For example, if a player stands on the tee of a par 4 that is 375 yards long, their expected score for the hole for their skill level would be 4.0 strokes.  Assume they hit a strong drive of 275 yards, and land in the fairway.  Now their expected score for the hole might be 3.8.  Since their expected score went from 4.0 to 3.8 as a result of the drive, they gained .2 strokes with the drive.

If you repeat this for every shot in a round of golf, you would gain a picture of strokes gained for the overall round.

One key to strokes gained is what an expected score is for each hole.  This was first calculated for tour pro players when shot by shot stats were available via the ShotLink system used in pro events.  With the advent of consumer-level shot tracking systems, it is now possible to generated expected scores for virtually all levels of golfers, and thus any golfer can track strokes gained for their round, as compared to any level of golfer.

Strokes gained is typically further broken down into 4 categories : Off the tee, approach, around the green, and putting.

The insights available once strokes gained was available has allowed insights into what really allows golfer to separate themselves from their competition.  Most notably, strokes gained was able to show that skill in driving is much more of a separator than is putting skill.  This went against many decades of conventional wisdom.