I think the market supply curve is a mystery to most economics students.  The demand curve is more intuitive because, well, we are all demanders of goods but few of us are suppliers/producers of a good. 

The supply curve on a graph reflects two things at the same time.  The market price received by the producer (determined by Demand) AND the cost of producing a good. Specifically, regarding the last point, the marginal cost of producing one more unit of a good (movement ALONG the supply curve). Marginal cost is the additional cost in labor and materials needed to produce that extra unit. 

In the market graph below I show the demand curve intersecting the supply curve at the "crook" of the supply curve.  At point "A" the quantity demanded = quantity supplied at 1,000 units.  I use point "A" as the current Full Capacity