1. Superior putting
2. Overall good ball-striking
3. Getting up and down around the greens
4. Decent length (for you) and accuracy off the tee
5. Understanding and navigating the golf course's architecture
6. Avoiding OB, lost balls and water hazards
7. Recoveries
8. Avoiding courses that are ill-suited for your game
9. Favorable conditioning
Some of these are inter-related. When I'm having a good ball striking round, I'm generally hitting the ball off the tee in good locations, hitting greens and avoiding OB, hazards, etc. Getting up and down around the greens often involve holing difficult par putts. My worst rounds occur when I am not striking the ball well, leading to lost ball penalties, difficult shots from rough/bunker.
However, My lowest rounds are when I make putts, whether they are for birdie, a difficult two putt (avoiding 3 putts), or par saves.
I did rank understanding golf architecture for the course (the architect's intent on the hole) as an important element, as they frame my approach to tee shot, approach shot, putting and short game. I have found that when I play a course the second time, I often score better, as I understand the layout, playing lines, green countours and adjust my game accordingly.