What does Adam Smith's "invisible hand" theory mean? Can you provide a relevant example?

Consumers’ desires certainly play a role in Smith’s theory, but I would argue it is more accurate to identify the “invisible hand” as a mechanism within the capitalist market. This includes not only consumers but also other companies that produce their own goods or offer their own services.

Consumer demand is part of the explanation for describing how the “invisible hand” operates, but this demand interacts with the capacity of companies to produce what they need. Take the following very basic example. Ten people want to buy a pair of trousers, but the company that makes them has only been able to supply five pairs. A businessman takes note of this situation and sets up his own company to make trousers, because he understands that the demand for trousers is greater than the supply. The next time ten people want to buy trousers, there are twelve pairs in the shop due to increased production. The original company is only able to sell three pairs of trousers, meaning that two pairs remain unsold. The first company reviews its strategy and decides to invest part of its capital in the production of coats, because the entry of the second company into the trouser market has created an oversupply of goods.

In both the fictional examples above, the end result is that businesses are able to supply goods to consumers in sufficient quantities. In the first case, this takes place because of a business decision to invest in an area where the demand for goods (trousers) currently outstrips supply, while in the second, the oversupply of a particular product (trousers) is counteracted by the decision of a company to reduce production and offer a new commodity to the consumer (coats).

Smith would argue that in both of these examples, the “invisible hand” of the market made these decisions possible. It enabled business owners to determine what the needs of consumers are and what their companies should therefore produce. It also encouraged businesses to develop new products when the demand for other products had been met, thus providing consumers with a wider selection of commodities. Advocates of Smith’s free market capitalist position believe the “invisible hand” of the market is far more efficient than, say, a government-directed planned program, such as the one that existed in the Soviet Union.

The idea of the invisible hand is the basic idea of laissez faire capitalism.  According to this idea, a capitalist society functions without anyone in control of it.  There is no "visible hand" telling companies what to make as there is in a more command-style economy.  Instead, entrepreneurs try to get rich by producing something they think customers will want.  Customers then determine what companies and products will survive.  They do this by either buying or not buying the companies' products.  Thus, there is an invisible hand (of consumers' will) that determines what happens in our economy.

An example of this would be Facebook.  No government official ever decreed "make a social networking site."  Instead, some people had an idea and tried it out.  The invisible hand of consumers started to use it.  When this was seen, advertisers started to use Facebook also.  In this way, Facebook became economically viable without anyone ever ordering it to be so.

Can you explain Adam Smith's concept of the 'invisible hand'?

The invisible hand that Smith wrote about is really just a metaphor for a market economy.  In such an economy, no one person or government entity really makes decisions about what will be produced and what will be consumed.  Yet, somehow, suppliers know what products to make.  Thus, the changes in a market economy are made by an "invisible hand" because there is no identifiable decision-maker.

In a market economy, the cumulative decisions of all consumers determine which things will be produced.  There is no central authority (that would be a visible hand) ordering businesses to make various things.  Instead, the consumers' decisions tell suppliers (in an invisible way) what sorts of things they should make because those decisions tell them what products can be most profitably sold.