An electrostatic charge buildup can cause radio frequency (RF) noise that may interfere with VHF communications and navigation receivers, ADF, and other avionics. RF noise is heard as a loud background hissing when transmitting or listening on the communications receiver. If the static discharge is strong enough, it may even desensitize an avionics receiver to the point where it will not function.
Static wicks are designed to bleed electrostatic charge off into the slipstream before it can build to the point of interfering with avionics. Generally, the faster the airplane the greater the potential for electrostatic buildup. However, even light general aviation aircraft are subject to the phenomenon. If the airplane you fly isn't fitted with static wicks, take a walk around the ramp-you'll see plenty of aircraft that are.
There is a science to the number and placement of static wicks. That's a job for the avionics shop. What you should be concerned with is that the wicks attached to the airplane you fly are in good shape, not broken or excessively frayed. This is especially important if you are an instrument-rated pilot and will be flying in visible moisture.
If you discover problems with static wicks during your preflight inspection, report them to the owner or operator of the aircraft. And don't forget to avoid walking into them during your preflight.