In this overview, we will examine the different features of a lever and break it down. But before we start, let's figure out how a radial master works in a really simple diagram...
Ok, to sum up this diagram, you pull the lever towards you and it pushes a plunger through a cylinder. That plunger squeezes out brake fluid out of the cylinder, down your brake hoses and into your calipers. The brake fluid in the calipers push the brake pads into the rotors, causing them to grab onto the brake rotors, thus causing you to slow down or stop.

Hey, let's stop and take a look at this lever design - it'll explain why most aftermarket master are radial. Notice the direction of the plunger and the direction that the lever travels. With a radial master cylinder, the plunger travels in the same direction as the lever. In a "conventional" master cylinder, the plunger actually travels perpendicular (or pretty close to perpendicular) from the direction of the lever. It makes sense that you can get a better feel for the lever if it's going in the same direction as the piston and plunger (radial) rather than going off on some funky angle (conventional). This is the main advantage of the radial design.