The factory radio uses a specific wiring harness connector, and aftermarket radios use a different one. The adapter acts as a bridge, connecting the car's wiring to the new radio's wiring. These are readily available at most auto parts stores and online retailers. They're often referred to as a "radio harness," "wiring harness adapter," or sometimes a "Metra kit" (as Metra is a common manufacturer).
You might also need an antenna adapter if the factory antenna connector is a different type than the aftermarket radio's. This is also commonly sold separately.
In short: You don't need a "special harness for the radio," but you *do* need a wiring harness adapter to connect the car's electrical system to the new aftermarket radio.
