Let's imagine you are playing a 446 yards par-4. The PGA Tour's scoring average, or benchmark, for a shot from 446 yards from the tee (remember, distance and location are the key variables) is 4.1 shots.
You hit a great drive and leave the ball in the fairway 116 yards from the hole. We go the benchmark again and we find that in the PGA Tour the scoring average from 116 yards on the fairway is 2.825.
How good was your drive? From the tee, your scoring average was 4.1, but after the first shot you were in a position where the scoring average was 2.825. If you subtract those numbers, you get 4.1 - 2.825 - 1 = 0.275, which means you "gained" 0.275 shots, a great drive!
Your second shot takes the ball to 16' 11" on the green, which means you go from a benchmark of 2.825 shots to 1.826 shots, your strokes gained is 2.825 - 1.826 - 1 = -0.001, which means that was just like the average shot in the PGA Tour.
The average score from 16' 11" on the green is 1.826, but you hole the putt, which means your strokes gained for this shot were 1.826 - 0 - 1 = +0.826, a really great putt for birdie.
If you want to play around with different lies and distances, we have a Strokes Gained Calculator that will help you understand everything, have fun with it!