Supply refers to the various quantities offered for sale at various prices. According to the Law of Supply, more of a good will be supplied the higher its price, other things constant or less of a good will be supplied the lower its price, other things remaining constant.
Price regulates quantity supplied just as it regulates quantity demanded. In graphical terms supply refers to the entire supply curve because a supply curve tells us how much will be offered for sale at various prices. Quantity supplied refers to a point on a supply curve. When the price of a good rises, individuals and firms can rearrange their activities in order to supply more of that good to the market, substituting production of that good for production of other goods.
With the firms, there is another explanation. Assuming firm’s costs are constant, higher price means higher profits (the difference between a firm’s revenues and its costs). The expectation of those higher profits leads it to increase output as price rises, which is what the law of supply states.
The law of supply also assumes that other things are held constant. Other variables might change causing a shift in supply.
As with market demand, market supply is the summation of all individual supplies at a given price. The market supply curve is the horizontal sum of the individual supply curve.