In the capitalist mode of production, social classes are based off of the relation between ownership and operation of private property and the means of production. Understanding and analysing class division and struggle is very important in understanding the nature of capitalism.
In capitalism, there are two main classes; the bourgeoisie and proletariat. They can both be broken down to two subclasses. In the bourgeoisie there are industrialists and the petite bourgeoisie. In the proletariat there is the labour aristocracy and the commoners. There is also an underclass, called the Lumpenproletariat.
The bourgeoisie is the employing class, the property holding class. The members of the bourgeoisie own capital, or assets which have the potential for the creation of more wealth. This capital is in the form of the means of production ( factories, machinery, farmland etc) and other forms of private property (something owned which can be used to exploit others). An industrialist is someone who owns a lot of private property and the means of production. Their income is made from this ownership. Despite owning the means of production, industrialists do not operate it. Instead they hire people who do not own the means of production to operate it for them.
The petite bourgeoisie is made up of small business owners and the self employed. They own some of the means of production and they do operate it. However, they also tend to hire workers to boost their profits. A decent portion of their income comes from their own labour, while the rest comes the exploiting the labour of a few others.
The proletariat is all people who do not own the means of production or any other form of private property. They sell their labour-power (the ability to work) to someone who does own it in order to live. They operate the means of production for wages.
The labour aristocracy is made up of workers who strongly benefit from super-profits extracted from ordinary workers. Most members of this subclass are actors, doctors, lawyers, or very skilled workers.
The commoners are simply ordinary people. They have only one valuable asset, labour-power, and only labour-power. Their psychical and intellectual labour goes to the production of commodities (goods which are bought and sold) and the capitalist sells the commodities produced by their workers for profit. After all production costs have been paid, the capitalist pays the workers only part of the amount of value added to the raw materials the commodities were made from, thus leading to an exploitive social relationship between the bourgeoisie and the proletariat.
The Lumpenproletariat is the social underclass of society. Members of this class neither own property nor operate it. It is composed of pickpockets, prostitutes, burglars, beggars, loansharks, and mobsters. Their income is made through preying on the proletariat.
Socialism is Humanism! 