Bicycle motocross (BMX) came about in the 1970s, when young people in Southern California began racing bicycles on dirt tracks. The sport's growth over the years has brought on the development of a specific make of BMX bicycle. Though these models differ depending on their use in racing or for stunts, they typically have a single gear and are built low to the ground. Any unnatural noise on any bicycle is a cause for concern; if you hear a clicking from the rear wheel of your BMX bike, you must diagnose the problem.
Lift your BMX off the ground, and spin the back wheel. If you don't hear the clicking like you do when riding, the issue probably stems from loose spokes. A wheel without enough tension can cause spokes to rub against each other when the rider applies weight to the bike.
Note whether the clicking occurs only when the bike is in low gear, if your BMX has multiple gearing. If so, the likely culprit is the chain rubbing against the spoke protector. If so, the spoke protector is probably bent or broken; replace it.
Note whether the clicking occurs only when you pedal. If so, check the cassette on the free hub body. Either the cassette or the freewheel bearings will likely have become loose. Tighten both for good measure (the tool to use will depend on your bike). Check that you aren't missing a spacer on your cassette and that the cassette is the right size for your BMX.
Pick up your bike and spin the wheel. If you have rear brakes, the brake pad may be out of alignment and rubbing against the rim of your wheel, most likely caused by a wheel that has gone out of true (that is, the rim is out of alignment, causing wobbling) or brakes that require realignment. Adjust these components if necessary.