Put simply, price is the amount of money needed to buy a particular good, service, or resource. In economics it's one of the most powerful forces. Everything but price can cause a supply or a demand curve to shift (price only changes a place on the curve).
Because goods are scarce relative to the demand for them, prices are used to determine who gets what goods. Therefore, because of price, a consumer, with a limited amount of money himself/herself, must decide what is the proper price of a good or service, depending on its utility (this is also known as the Income Effect). It also helps a consumer to understand scarcity. Likewise, a company must look at the price of a good it wishes to produce to see how much they should produce, if any at all.
We can also look at the rationing function of prices. Let's say there are two toothbrushes, BrushMe and OralBrush, and that the former costs $3 and the latter costs $22 (both brushes are exactly the same). Most people will pick BrushMe beause its the cheapest, forcing the makers of OralBrush to drop their price. Those who do not have at least $3 will not be able to brush their teeth, thus allowing them to rot away and that makes the market for toothbrushes shrink. If there is a significant number of people who cannot afford the $3, and BrushMe (or OralBrush) thus cannot make any profits, both will be forced to lower their prices.
Contrary to common sense, a price is determined by the market, including all sellers of a good or service and their buyers. Although firms technically set the price, it is the wax and wane of consumer demand and product supply that force the firm to pick the appropriate price.