A central mechanism behind the invisible-hand story is the price system. Prices summarise information about scarcity and demand that is scattered across millions of people.
When a good becomes harder to obtain relative to how much people want it, its price tends to rise. Higher prices give buyers a reason to use less or switch to substitutes, and give producers a reason to supply more. When supply is plentiful, prices tend to fall, encouraging greater use and discouraging excess production.
No central office needs to know every detail of weather, technology, and preference for this process to operate. That is why economists often describe prices as signals and incentives at once. The system is imperfect: bubbles, monopolies, missing markets, and external costs can distort signals. Understanding both the signalling role of prices and these distortions is part of learning the economics of the invisible hand.