There are so many parts of the golf swing that are important, it's hard to single out one part and say it's the most important. So I will say that a major part is the transition from the backswing to the downswing. This is where all the good work you have done so far, set up correctly, swung back correctly, can be made use of or thrown away.
There are two issues here. First, you're changing the direction of your swing movement. What is the first thing that moves? What leads off the downswing? Second, you don't hit the ball with your backswing. You don't hit it with the early part of your downswing, either, so you need to find a way to keep from getting ahead of yourself -- trying to hit before it's the right time. The temptation to do that is great, and many recreational golfers give in.
So. You've wound yourself up to the left, and now you're ready to start unwinding. Make the first move down with your lower body, on the right side. By lower body I mean from the hips down.
What part of your lower body you move first is up to you, because the entire thing moves as one piece. You can move your right knee toward the ball to get everything going, you can slide your right hip to the right a bit, or, if your right foot comes off the ground a bit on your backswing, you can plant the foot on the ground again for your first move. As soon as that one thing moves, though, the rest of the right side follows.
To solve the second problem, keep the orientation of your upper body the same in the early part of the downswing. That is, your entire upper body feels like it is in a cast and is merely being carried around by the turning of the lower body. It will all unfold in time.
Practice your transition by swinging back, then applying your right-side trigger. Swing down only to where your hands are about as high as your left hip, and stop. You should have the majority of your weight tending toward the right side, and while the angle between your right arm and shoulder line has started to open up, the angle between your right forearm and the clubshaft should be the same.
Practice this a lot. It's how to turn a hit into a swing, which is the way to better ballstriking.