A highly skilled player could go out and 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.
No matter what your handicap or skill level, having the right clubs 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 (swingweight, club length, grip size, grip material, shaft flex, shaft material, loft and lie, clubhead style, clubhead material, and so on). The two most important of these are: lie angle (the angle between the shaft and sole plate)
and shaft flex (the relative stiffness or softness of the shaft).
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.