The key to understanding Marx is his class definition.1 A class is defined by the ownership of property. Such ownership vests a person with the power to exclude others from the property and to use it for personal purposes. In relation to property there are three great classes of society: the bourgeoisie (who own the means of production such as machinery and factory buildings, and whose source of income is profit), landowners (whose income is rent), and the proletariat (who own their labor and sell it for a wage).
Class thus is determined by property, not by income or status. These are determined by distribution and consumption, which itself ultimately reflects the production and power relations of classes. The social conditions of bourgeoisie production are defined by bourgeois property. Class is therefore a theoretical and formal relationship among individuals.
The force transforming latent class membership into a struggle of classes is class interest. Out of similar class situations, individuals come to act similarly. They develop a mutual dependence, a community, a shared interest interrelated with a common income of profit or of wages. From this common interest classes are formed, and for Marx, individuals form classes to the extent that their interests engage them in a struggle with the opposite class.
As Marx saw the development of class conflict, the struggle between classes was initially confined to individual factories. Eventually, given the maturing of capitalism, the growing disparity between life conditions of bourgeoisie and proletariat, and the increasing homogenization within each class, individual struggles become generalized to coalitions across factories. Increasingly class conflict is manifested at the societal level. Class consciousness is increased, common interests and policies are organized, and the use of and struggle for political power occurs. Classes become political forces.
The distribution of political power is determined by power over production (i.e., capital). Capital confers political power, which the bourgeois class uses to legitimatize and protect their property and consequent social relations. Class relations are political, and in the mature capitalist society, the state's business is that of the bourgeoisie. Moreover, the intellectual basis of state rule, the ideas justifying the use of state power and its distribution, are those of the ruling class. The intellectual-social culture is merely a superstructure resting on the relation of production, on ownership of the means of production.
Finally, the division between classes will widen and the condition of the exploited worker will deteriorate so badly that social structure collapses: the class struggle is transformed into a proletarian revolution. The workers' triumph will eliminate the basis of class division in property through public ownership of the means of production. With the basis of classes thus wiped away, a classless society will ensue (by definition), and since political power to protect the bourgeoisie against the workers is unnecessary, political authority and the state will wither away.