What is cross bridge cycling and why is it important in muscle contraction?

In order to understand cross bridge cycling and its importance in muscle contraction, you need to be familiar with the ‘contractile machinery’ that causes muscle contraction and the sliding filament theory. To briefly recap, muscle contraction occurs when the thin filament, actin, slides past the thick filament, myosin - This is essentially the sliding filament theory.  The mechanism that causes the actin filaments to slide past myosin in skeletal muscle in brief is as follows:
 remembering that a sarcomere is the stretch of myofibril between two z lines where myosin in central and an actin filament is both above and below the myofibril on each side of it, with its medial side slightly overlapping myosin and its lateral side attached firmly to the z line .
Nerve impulse arrives at muscle, causing release of calcium from the sarcoplasmic reticulum of muscle fibre
Troponin is bound to tropomyosin which is bound to actin. When the muscle is at rest, tropomyosin is sitting in such a position, that it is covering the binding sites for myosin heads on actin.
Calcium bind to troponin. This causes it to undergo a conformational change which pulls the tropomyosin it is attached to out of its resting position, exposing binding sites for myosin heads on actin.
Myosin heads covalently bind to the exposed binding sites.
 The myosin head undergoes a conformational change which pulls the actin along.
It then releases the actin, returns to its original conformation, extending out laterally again and forms a bind with another actin binding site that is further along the actin and closer to the z line. This repeated motion is what causes the sliding of the actin filament past myosin.
Cross bridge cycling refers specifically to the action of the cross bridge, that being the head and hinge region of the myosin filament. It is essentially acting like a bridge when the head is covalently bonded to actin, and this bridge is continuously being formed and broken during muscle contraction-the cross bridges are being cycled, and it is this action which is allowing for the filaments to slide the way they do.
The cross bridge cycle can be broken down as follows:
Hydrolysis of ATP to ADP and Pi, with products still covalently bonded to myosin, cause it to enter an energised state.
Cross bridge binds to actin. It undergoes a conformational change. ADP and Pi are released. You then get a power stroke (ie cross bridge moves, pulling actin along which causes the power stroke (ie the cross bridge moves pulling the actin along)
ATP binds to myosin, causing cross bridge to detach.
The process starts again.