What is the purpose of the slack adjuster on the air brake system?

It takes up the slack in the brake system as the pad lining and system components ware. The S-cams have bushings that ware out (get egged shaped) creating more clearance, the pads ware do to their function, the clevis pins on the slack adjuster ware. The device rotates the S-cam further to take up that slack. They are also a lever, they add mechanical advantage. Typical slacks are 5.5 and 6.5 from pin center to S-cam center. Multiply the force that a brake chamber rod is exerting by the length of the slack to get applied force. Example, a 30 in brake chamber with 20 psi applied will push with 600 psi of force. Multiply by the lever arm at 5.5 inches gives you 3300 in. pounds of torque. Divide by 12 to get ft. lbs = 275 ft. lbs.