| In England, a "state school" is a primary or secondary school paid for by the government, as opposed to a "public school," which is usually what Americans would call a "private school."
Back in the USA, a "state school" is a university funded by a state government. While most private universities charge annual tuition fees in the neighborhood of $20,000 to $30,000, a typical state school might charge $5,000 a year for residents of the state and $15,000 a year for everyone else.
Most states have several state schools (Wyoming is the only exception). In most cases, the main state school in a given state is called the "University of (insert state name here)." There are exceptions, though: the University of Pennsylvania is actually private (and a member of the Ivy League), while New Jersey has Rutgers and New York has the State University of New York (SUNY).
While state schools tend to have a reputation for handling the academic middle class, a handful are actually among the top universities in the US. These would include:
The vast majority of public universities in the US are state schools. The only federal universities are the military academies, and municipal universities are only found in a handful of cities. | 
