how does price provide information that influences the behavior of consumers and producers in a market?

Price is the amount of money or compensation for a good or service. If a seller of a product or service possess a monopolistic power (is the only one offering said product or service) that seller is a "price maker". When the price is set through the normal (supply and demand) the price is thus set, and it is a situation of "price takers". Consumers and producers behaviour are normally influenced by these price settings.