Marx believed that in order to understand the nature of a society, one had to understand its economic base. The word "infrastructure" essentially refers to this base, which Marx defined as the relationship of people to the means of production. Under a capitalist system, the "infrastructure" was private ownership of the means of production by the bourgeoisie, which, due to relentless mechinization and other developments, forced more and more people into wage labor. "Superstructure" is a Marxian term referring to culture, including systems of belief, societal mores, and even some aspects of government and law not directly related to property relations. Marxists argue, to varying degrees, that the superstructure is determined by (and, from an academic perspective, explained by) the economic relations that lay at the heart of the base, or infrastructure. So from the standpoint of literary criticism, a work itself cannot really be understood on its own, but as part of a web of cultural relations that constituted a superstructure, that is in turn affected by the infrastructure.
Marx was a philosopher of history essentially. His philosophy has been called historical materialism and dialectical materialism. The former conveys the idea that history is dictated by actual material events: social, political, and economic interactions. The latter, dialectic, conveys the idea that this progress of materialism is based upon a dual (and/or dueling) system. This system of two forces working with or against each other is called a dialectic. Dialectics goes back to Aristotle and the ancient Greeks as a factor in philosophy. And Marx uses dialectics to describe forces which work together and/or against one another. The proletariat and the bourgeoisie, or the workers and the owning class, are at odds with each other but under a capitalist system, they work together (according to Marx, to the dismay of the proletariat).
Likewise, Marx applies the dialectic to describe the mechanism of life in two structures: the infrastructure (base) and the superstructure. The infrastructure is made up of the forces, the means, and the relations of production: the material "stuff" of life. The infrastructure comprises 1) Forces: the workers, the technical knowledge to perform the work (training, knowledge), 2) Means: the actual materials of production (raw materials, machines, tools), and 3) Relations: the interactions between workers as well as between workers and business owners. Of course, there are potential clashes between workers and owners, but it is ultimately through the forces of production that real change occurs.
The superstructure arises from the infrastructure. The superstructure can loosely be defined as culture. But what makes it important in Marx's thinking (in this dialectic of infrastructure and superstructure) is that this superstructure comes from the infrastructure and reconditions ways of life/living so that the infrastructure continues to be produced. It is dialectic but cyclical in a way. The infrastructure (material things and interactions of life) produce a culture (laws, politics, art, etc.) and that culture then is structured in such a way that the society continues to reproduce the infrastructure. For change (or a revolution to occur), something must change in the infrastructure - it would then affect the superstructure, which would then effectively change the infrastructure.