Service the brake cables on your bike if it is rubbing or not functioning properly.
Lubricate the caliper pivot.
Check the adjustment of your brake cables. When the brakes are not applied, they should be about 1/4 inch from the wheel rim, and when the lever is squeezed, they should make full contact at about half the distance the lever will travel.
Lubricate the cables. You may use a lubricant in an aerosol can with a tube to spray oil into the cable housing at the ferrel where the cable enters the housing underneath the brake levers. A light machine oil with a small nozzle similar to "3 in 1" Oil, or a special brake cable oil purchased at a bike shop is recommended. WD-40, and similar products may "wash" the factory lubricant off the cable, and when they evaporate, there will be very little lubricant residue on the cable.
Remove the cable from its casing, only if it is very stiff, or difficult to operate. This is done by removing the clamp at either the caliper or brake lever, and pulling it out the opposite end. If you remove the cable, use an aerosol solvent (or even WD-40) to flush any dirt or debris from the cable tube while the cable is out. Apply a light coat of lithium grease or machine oil to the cable, and reinstall it if it is not damaged.
Thread the loose end of the cable through the clamp at the end you removed previously, and check the "free travel" (the distance the brake lever can be squeezed before the brake contacts the wheel). When the brake pads are about 1/4 inch from the wheel with the lever released, tighten the clamp.
Replace either the cable, or the complete cable assembly if the steps above did not solve the problem of the cable not moving when the brakes are applied. Buy the same diameter cable, factory fitted, in the same length as the original equipment. Making up the ferrels, cutting the cables to the correct length, and threading cables cut with pliers through the clamps is a difficult chore.