In order to define how much quantity of a certain product to bring to the market, each firm tries to maximize its profits. The quantity finally brought to the market is the one that, actually, maximizes the profits. That maximization, in a perfect competitive market, consists on setting the marginal costs equal to the market price.

Now, the amount that a single firm brings to the market is nothing but the individual supply. In order to get the market supply, we need to aggregate the individual supplies of all the firms of the market. This may be quite complicate. In microeconomics, in order to simplify the analysis, we work with the assumption of the "representative agent". This means that, once one of the firms maximizes its profits and we come up with the optimal individual supply, we just multiply this individual supply by the amount of firms in the market. This way, we reach the market demand.

In consequence, the difference between market supply and individual supply is just that the market supply consists on the aggregation of all the individual supplies of the market.