Front suspension looks basically like this
The coil spring has a shock absorber in the middle. Often called struts because the body of the shock has structure importance for the coil spring. Also called coilovers. All that does is control the ride height and absorb bumps. The A shaped parts are called upper and lower control arms and these define the location of everything. They rotate up and down and keep the wheel mostly upright as that happens. When you lift above a certain point, control arms need to be modified or replace in order to allow more suspension travel because the factory parts have a set range of motion. The coil spring and the strut are the main items that control the amount of lift you get. A coil spring with more turns, or thicker wire diameter than stock will provide greater increase to compression, resulting in keeping the vehicle weight higher off the ground.
Rear suspension looks basically like this.
The coil springs perform the same function as the front, but the shock absorber is independent. The upper and lower links (control arms) in this case are basically straight rods connected to the axle housing at one end and the chassis at the other. These control arms keep the axle housing in place but allow vertical motion. The longer they are, the more range of motion you have, providing the springs and shock are also longer. Another item not show is the panhard bar and locates the axle housing left to right.