Adam Smith furthered the ideology of the laissez-faire or capitalist economy in which a free market exists and private businesses are separate and only somewhat regulated by the state. The industrial revolution depended upon a capitalist economy in which bosses/owners profit off the work of a laboring class of people who produce the goods/materials that the owner profits from. The Industrial Revolution drastically increased class divisions as a class of entrepreneurs and business owners became wealthy off paying laborers meager wages.

Adam Smith claimed that the "invisible hand" of competition and demand would allow the free market to grow and succeed without government interference. With the rise of the Industrial Revolution and the Market Revolution, this "invisible hand" was, in reality, the steady stream of workers who were forced to accept tiny wages, immensely bad working conditions, and long work hours to afford basic food and shelter necessities.

By commodifying shelter, food, and other basic necessities, capitalism ensures a constant stream of workers who must constantly work paycheck to paycheck to buy from the owning class access to necessities and resources that come from the Earth and should be free. With the rise of the Victorian era middle class, demand existed for the products and materials created by the working class who were trapped in an endless cycle of labor in order to survive. Without any interference, company owners could slash costs of production by paying meager wages, cutting corners in product quality, and allowing incredibly unsafe (but cheaper for the company) working conditions.

Adam Smith's Wealth of Nations was a seminal work in the early Industrial Revolution in Great Britain. With this book, Smith helped to lay the ideological (and therefore policy) foundations for the development of capitalism. These included the idea that government interference (tariffs, subsidies, regulations, and so on) was counterproductive to economic growth. In a famous chapter on the regulation of woolen textile imports, Smith claimed that if left alone, the "invisible hand" of economic self-interest would guide businessmen, merchants, and manufacturers to make the best possible economic decisions. These decisions would in turn help the economy grow to a far greater extent than the mercantilist attempts to exclude imports from foreign nations. 

Smith also demonstrated the importance of division of labor to optimizing production in a nation. Using an example of a pin factory, Smith showed that dividing a task up into simple, easily repeated actions would maximize productivity. He cautioned that workers in such a system would become easily bored, and pointed to the importance of education, but still, his thoughts on division of labor presaged the factory model that dominated the Industrial Revolution in the Western world. Smith's economic theory, especially his disdain for government intervention in the economy, remained profoundly influential throughout the nineteenth and early twentieth centuries.

Adam Smith was the father of capitalism, the theory that individuals should own the means of production and government should not become involved. It was because of his thinking that private business enterprises were allowed to develop unhindered with their sole motive being profit.

Smith was the author of An Inquiry into the Causes of the Wealth of Nations. He opposed the old theory of Mercantilism and suggested private ownership of enterprise instead. His argument was that government should only provide those services which could not be offered by private enterprise for profit, primarily national defense and public services such as police protection and water and sewer. He illustrated the operation of the factory system by describing a pin factory:

One man draws out the wire, another straights it, a third cuts it, a fourth points it, a fifth grinds it at the top for receiving the head….and the important business of making a pin in this manner, divided into about eighteen distinct operations

Adam Smith was important to the Industrial Revolution because he was the most important thinker behind the idea of laissez-faire economics.  In other words, he wanted the government to stop trying to tell businesses what to do.  Instead, he wanted the "invisible hand" of competition and consumer choice to tell businesses what to do.

Smith was also an advocate of the idea of division of labor.  In a system with division of labor, each worker does only one task or a few tasks in the process of making a larger thing.  Instead of having one worker make a whole shoe, for example, you have one worker just cut out the pieces all day long.  Or you have one just sew the tongues on the shoes.  This means that the person only has to master one skill and things can be done more efficiently.

These two ideas were both very important for the Industrial Revolution.  The first of them encouraged governments to let businesses do what they wanted instead of telling them what to do.  The second helped businesses understand the best way to get more efficiency out of their workers.