Basically speaking, Marx says that the "base" is the foundation of our society. It is the thing that is truly important. By contrast, the superstructure consists of things that are built upon that base.
Marx argued that what was truly important in any society was the "relations of production." In other words, it is the relationship between those who do the work and those who own the means of production that really determines how a society is.
On top of that base, there is a superstructure that seems to be what is important about our society. This consists of things like our structure of government or our culture. These are things that seem really important but aren't. What is really important is what the relationship is between those who work and those who own the means of production.