What is meant by Adam Smith's "invisible hand" theory? Can you suggest an example where this seems true & economics works that way?

The Idea of "invisible hand" was introduced by Adam Smith in his book Wealth of Nations first published in 1776. Smith uses this concept to describe a paradox of laizzes-faire or perfect completion, in which every person in an economy working to achieve his own selfish goals leads to benefit of all.The individual neither intends to promote the public nor he knows how much he is promoting it.Adam Smith compares this process as an invisible benevolent directing the whole process for benefit of all.

Based on belief of effectiveness of this so called invisible hand, the doctrine of laissez-faire which recommends that government should interfere as little as possible in economic affairs, guided the action of governments in many countries. However, beginning from the twentieth century, there has been growing feeling that the theoretical assumption on which the action of invisible hand is dependent, do not exist in reality.

It is not possible to give examples of the working of invisible hand as it applies to complete economies. However we can say that till start of the industrial revolution, this was the primary mechanism at work for the economic development and growth all over the world.