Definition: Fly the Green/Flew the Green
The different forms of that phrase all simply mean hitting your golf ball over the green. If you are playing an approach shot and your golf balls winds up behind or beyond the green because you hit it too far, then you "flew the green."
Flying the green can be caused by misclubbing (in this meaning using too much club for the shot you faced); by mis-hitting the golf ball (e.g., catching it thin and hitting a low screamer that bounds over the back of the green); or, sometimes, by playing from an iffy lie where you just aren't sure how the ball will react at contact.
Why is flying the green something that recreational golfers are so afraid of? It probably stems from the fact that many greens are elevated or at least slightly raised above the surrounding turf, so that golfers will often not have a clear view of what is behind a green. What we can't see worries us more than what we can see.
Also, it is common on golf courses for many greens to be tilted, at least a little, from back-to-front. If your ball winds up behind such a green, then you'll be playing a chip or pitch or bump-and-run to a green that runs away from you.
Today most golfers have access to golf GPS data or, at least, a yardage book or pin sheet. If you have access to one of those things, you'll be able to see before playing a shot what lies over the green, and how wary of flying the green you should be.
But, just to recap: "Fly the green," "flew the green," "flying the green" — they all mean hitting your golf ball over the putting green.
Related terms: