Coilovers combine the spring and shock into one threaded-body unit that has continuous height adjustment. Coilovers are very common on race cars and other track applications where performance is the primary consideration and other variables (noise, maintenance) come second.
Most coilovers feature a threaded shock body with a spring perch that is threaded onto the shock. You turn a threaded spring perch to raise or lower the car ride height.
Some coilovers include adjustable shocks as well, so you can adjust the damping firmness as well as the ride height. Setups like this are perfect for a track car, because you can tailor the suspension to the track conditions. It's also great for a weekend warrior -- soft damping on commute days, firm on track days!
Fancier coilovers feature advanced damper technology, like inverted monotube (instead of the standard twin-tube) construction, remote reservoirs for superior heat management, and multiple independent adjustments of rebound and compression damping.
Coilovers do have their drawbacks. They generally will transmit exhibit higher noise/vibration/harshness (NVH) than traditional suspension, especially if they have solid-bushing pillow-ball upper mounts. They can require more maintenance than a traditional spring/shock setup. The threaded ride height adjusters can corrode with normal weather and road salt, resulting in the ride height no longer being adjustable. Some coilover designs also have significantly reduced suspension travel compared to standard suspensions, especially in the down (droop) directly.
If you are aware of and willing to live with the trade-offs, the coilover suspension is the most effective way to get your car suspension very low and very track-ready.