Smith wished to wipe away a whole system of government interference in trade that he believed to be both unjust and inefficient, rewarding poorly run businesses by protecting them from competition. He also thought that talented individuals were blocked from rising by a system that locked preexisting players into place.

Instead of government decision making, Smith proposed letting what he called the "invisible hand" of the market rule. If tariffs, monopolies, and unfair advantages to a few favorites were removed, he argued, everyone in the economic system would have a fairer chance. The invisible hand of trade would prove to be more efficient and better at choosing who deserved to thrive than government interference. Whole economies would benefit, and the wealth of nations be increased.

In The Wealth of Nations, first published in 1776 as An Inquiry Into the Nature and Causes of the Wealth of Nations, Adam Smith argues that though autonomous in principle, the individual relies on others for the necessities of life. These necessities cannot be obtained solely through the benevolence of others. One must secure them through some form of exchange by appealing to the self-interest (or self-love) of others. Put differently, in order to obtain a good, one must offer something useful in exchange. The freedom to produce in accordance with one's self-interest ensures the availability of goods in a society, both in terms of quantity and variety.

Monopolies and, to a lesser degree, restrictions on employment in certain fields, lead to high prices, which makes goods less accessible to individuals. By contrast, free trade and free competition establish lower prices; they also ensure that enough will be produced but not too much. If at any given moment, there is a dearth of a certain good, individuals will make up for that lack so as to benefit from the void in the market. If for a moment too much is produced, prices fall below the natural (or free market) rate, and production diminishes accordingly.

In other words, free competition and free trade establish a healthy balance of sorts, regulating the quantity of production in accordance with need, and bringing prices to a lower and fair level. Smith argues that this principle extends to all economic spheres: the freer and more general the competition, the more the public benefits, not only in the price of goods but also in the quality of services. Thus, in pursuing their own interests under a system of free trade and free competition, individuals end up benefiting the public.

Smith's The Wealth of Nations can be read in its entirety at the link provided below.

In The Wealth of Nations, Adam Smith argues that allowing individuals to pursue their own economic gains will help society as a whole because individuals will selfishly take actions that actually make society as a whole richer.  Smith, speaking of a man (in those days, there were no thoughts of treating women equally) who pursues his own economic interests, says

By pursuing his own interest he frequently promotes that of the society more effectually than when he really intends to promote it.

But how does this work?  Think about the way our capitalist societies work.  Someone like Steve Jobs wants to get rich so he tries his best to invent something that will make him a lot of money.  He comes up with things like the iPhone, which help us all.  Even the average person helps out in this way.  Because I want to make money, I do my best at my job.  By doing well at my job, I help my firm make money.   This helps me and it helps my firm, and it even helps the people who buy our services.

In these ways, people who are pursuing their own private interests actually end up helping society as a whole.  This is the great benefit of having a capitalist system.