No matter what your handicap or skill level, having clubs that fit you properly is one more thing you can do to give yourself the best possible chance of playing well.
There are many different variables in club fitting (swing weight, club length, grip size, grip material, shaft flex, shaft material, loft and lie angles, club head style, club head material, and more). Two of the most important of these are lie angle and shaft flex.
A highly skilled player could shoot a very good score with just about any set of golf clubs. They have enough feel and experience to make adjustments and adapt to the performance differences between clubs quickly.
For a middle to high handicap player, however, having equipment that is properly fitted to their physique and capabilities is more crucial.
If you're serious it's also important to have the frequency of your shafts consistent throughout your set. Good clubmakers will have no problem fitting you for these variables. Of course, there's no substitute for liking the look and feel of your equipment.