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I don't think I can explain this better than what is mentioned on Wikipedia already about the subject:
The invisible hand is a metaphor invented by Adam Smith to illustrate how those who seek wealth by following their individual self-interest, inadvertently stimulate the economy and assist society as a whole. In the general opinion, in The Wealth of Nations and other writings, Smith claims that, in capitalism, an individual pursuing his own good tends also to promote the good of his community, through principal that he called “the invisible hand” of the market, which ensures that those activities most beneficial and efficient will naturally be those most that are profitable.
Examples and arguments
A very simple real world example of how the invisible hand is supposed to work is the queue for a shop checkout. Each customer getting in line selfishly chooses to maximize his own interest, that is to checkout in the shortest time, regardless of the other customers. Their utility maximizing choice is to get in queue in the shortest line, this means that eventually customers queue up in lines all of the same length. Therefore even without the slightest direction and by following only their selfishness, the lines are all of the same length, which is clearly the most efficient disposition.
Since Smith’s time, the principle of the invisible hand has been further incorporated into economic theory. Leon Walras developed a four equation general equilibrium model which concludes that individual self-interest operating in a competitive market place produces the unique conditions under which a society’s total utility is maximized. Vilfredo Pareto used an edgeworth box contact line to illustrate a similar social optimality.
Ludwig von Mises, in Human Action (see note 3 at the bottom), claims that Smith believed that the invisible hand was that of God. He did not mean this as a criticism, since he held that secular reasoning leads to similar conclusions.
The invisible hand is traditionally understood as a concept in economics, but Robert Nozick argues in Anarchy, State and Utopia that substantively the same concept exists in a number of other areas of academic discourse under different names, notably Darwinian natural selection. In turn, Daniel Dennett has argued in Darwin’s Dangerous Idea that this represents a “universal acid” which may be applied to a number of seemingly disparate areas of philosophical enquiry (consciousness and free will in particular). See also Social Darwinism.
Criticism
High-profile US dissident Noam Chomsky points out that Smith's metaphor from this book is wildly taken out of context by many of today's mainstream economists:
Let's... keep to Adam Smith, a very important figure. He was pre-capitalist in his conceptions, and often quite interesting. For example, his basic argument for his rather nuanced views about markets: that under conditions of liberty they would lead to equality, an obvious desideratum. Or his one use of the term "invisible hand" in "Wealth of Nations," in an argument for what economic historians call "home bias," in effect an argument against what is now called "neoliberalism" or "neoclassical economics." Smith argued that the English economy, what he cared about, would be wrecked if British capitalists were to invest abroad and import from abroad, but it would not be a problem, because "home bias" would lead them to invest at home and use domestically-produced goods, and therefore, by an "invisible hand," Britain would be saved from the ravages of international markets. Or his argument against division of labor, and insistence that in any civilized society, governments would intervene to constrain it, because it would turn working people into creatures as stupid and ignorant as a human creature can be -- essentially on von Humboldt's assumptions. Yes, Smith is very much worth reading, whether one agrees with his interesting work or not. Reading, not worshipping on the basis of concocted mythology.
Further, Adam Smith himself frequently warned in Wealth of Nations about how the invisible hand can lead to disastrous outcomes (as Chomsky pointed out). For instance:
In the progress of the division of labour, the employment of the far greater part of those who live by labour, that is, of the great body of the people, comes to be confined to a few very simple operations, frequently to one or two. But the understandings of the greater part of men are necessarily formed by their ordinary employments. The man whose whole life is spent in performing a few simple operations, of which the effects are perhaps always the same, or very nearly the same, has no occasion to exert his understanding or to exercise his invention in finding out expedients for removing difficulties which never occur. He naturally loses, therefore, the habit of such exertion, and generally becomes as stupid and ignorant as it is possible for a human creature to become. The torpor of his mind renders him not only incapable of relishing or bearing a part in any rational conversation, but of conceiving any generous, noble, or tender sentiment, and consequently of forming any just judgment concerning many even of the ordinary duties of private life. Of the great and extensive interests of his country he is altogether incapable of judging, and unless very particular pains have been taken to render him otherwise, he is equally incapable of defending his country in war. The uniformity of his stationary life naturally corrupts the courage of his mind, and makes him regard with abhorrence the irregular, uncertain, and adventurous life of a soldier. It corrupts even the activity of his body, and renders him incapable of exerting his strength with vigour and perseverance in any other employment than that to which he has been bred. His dexterity at his own particular trade seems, in this manner, to be acquired at the expence of his intellectual, social, and martial virtues. But in every improved and civilized society this is the state into which the labouring poor, that is, the great body of the people, must necessarily fall, unless government takes some pains to prevent it.
Another critique could be that the actual grounds for the invisible hand "Every individual naturally inclines to employ his capital in the manner in which it is likely to afford the greatest support to domestic industry, and to give revenue and employment to the greatest number of people of his own country." is in public reduced to "Every individual naturally inclines to employ his capital in the manner in which it is likely to afford the greatest profit" and has most individuals acting accordingly, which does not include employing the greatest number of people in his own country with shortsighted(!) profit-maximising strategies.
At the wikipedia-site, there is even more on this subject.
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