Not all of us can afford that kind of investment, and many of us don't really need outer-limits speed capability and handling. So high-performance tires fill the gap between ultra-high and mass-market. High-performance tires aren't rated for ultimate speed ("only" 125-130 mph or so), but their construction gives them crisper handling response and better traction than the mass-market tires. They'll ride a little softer than the ultra-highs too, so they won't be as harsh over curbs and potholes. You can still pay dearly-maybe $150 or so per tire, depending on size-but you'll find tires in the $60-$70 range too.
All tires are made up of similar components, starting with the innerliner, which keeps the air inside the tire. Surrounding the innerliner is the tire's body, which is made up of fabric plies. The terms "radial" and "bias ply" refer to the orientation of these body plies. A radial tire's plies are perpendicular to the tread, while the plies in a bias-ply tire run diagonally ("on the bias"). You've heard of "steel-belted radials," right? That refers to belts that run under the tread area to strengthen and stabilize the tread. Around the outside of the tire are the sidewall, which gives the tire its lateral stiffness and protects the side of the tire from damage, and the tread, which is where the rubber meets the road. The bead, where the tire meets the wheel, consists of steel-wire hoops built into the sidewall.
As a tire's performance envelope increases, various components are beefed up to withstand the forces acting on it. For example, the centrifugal force at high road speeds can make the tire's belt package want to pull away from the rest of the tire. So companies reinforce their high-speed-rated tires with cap plies. Bridgestone, for example, uses nylon for its cap plies, as nylon shrinks when hot (speed generates heat) to fight those centrifugal forces.
High speeds also create bulges in a radial tire's sidewall. If that bulge happens too fast, or if a tire develops multiple sidewall bulges, the heat generated by the bulging can tear a tire apart. Tires with high speed ratings have extra reinforcement in the sidewalls to stiffen them and prevent high-speed bulges.
Now, both of those technical aspects have a benefit, even if you're not going 150 mph. Cap plies under a tire's tread help keep it flatter on the ground, which gives it a larger footprint and adds stability. A stiffer sidewall translates directly to crisper handling, since more of the cornering forces are actually changing the car's direction and not causing the sidewall to roll over. This is a difference you can feel even at 30 mph. Even if you're planning to keep your car at legal (or near-legal speeds), you can still benefit from a tire designed to go 130 mph or more.