Did you know that my last name is made up of economic graphs?

Let me explain. X is just a generic Demand and Supply graph. The U is an Average Cost graph of a firm. Together they determine the quantity supplied by a firm in a perfect competition.

In a perfect competition, there are a large number of firms producing a homogeneous good. Each firm is so small in relation to the market that the quantity supplied by the firm is trivial. Because of this, each individual firm can only sell at the market price. If they charge more, consumers will just buy from someone else. And since it can already sell everything it makes at the market price, there's no point in charging any less than the market price.

Since the firm cannot change the price it charge, the profit it makes depends solely on the quantity it produces. In the long run, a firm in perfect competition will always makes zero economic profit. That means the firm covers its cost and makes a reasonable return for its trouble. Because profit is average price minus average cost, and since firms produces (or at least tries to) at the lowest possible cost, the lowest point of a firms Average Cost lies on the market price. This point of interception is where the firm will produce.