A floating caliper has piston(s) on one side and slides back and forth on bushings or pins acting as a clamp. When you apply the brakes, the piston pushes the brake pad on the inboard side against the rotor. The caliper then slides on the bushings or pins and squeezes the outboard pad against the rotor. This causes the caliper to clamp" the rotor between the brake pads. With the piston(s) on the inboard side of the caliper it allows better clearance to the wheel as opposed to a fixed mount caliper.