The basic unit of the American public school system
is the school district, in which several schools in a geographical area operate under the authority of a single school district. The term "school district" may refer to the administrative apparatus or to this geographical area itself. Districts are usually governed by an elected school board
of five to a dozen citizens from within the district, although the board will sometimes hire full-time administrators to assist with and coordinate the day-to-day operations of the district.
School districts set a single curriculum for the district, hire and fire teachers, administrators, and school staff, purchase needed books, supplies, and equipment, and contract out for maintainence and upgrades of school buildings, as well as for the construction of new ones. In addition, they may contract out other services, such as transportation, sanitation, and food services. In many states, school districts are required to conduct a bid process for any purchase or contracting job, especially for expensive matters.
All of this requires money, of course. Many school districts are funded by local property taxes, which school districts usually have the power to impose and raise (though this power is sometimes subject to voter approval). In some states, school districts recieve funds directly from the state, usually on a per capita basis. Other funding sources include grants, advertising contracts, state lotteries, and soft drink sales concessions. School districts regularly issue bonds, especially to pay for new construction or capital improvement.
Although urban school districts may be in charge of up to several hundreds of schools (in which case the district is often carved into several administrative units), a school district is most commonly comprised of one or more towns with a single high school, one or more middle schools that feed into it, and one or more elementary schools that feed into them. These school districts may vary in size - 50 person graduating classes are not unheard of, but my school district, for example, had a graduating class of around 1200, coming from two high schools. (It is worth noting that this represents the largest school district in Pennsylvania outside of Philadelphia or Pittsburgh, and was created in the late 1960s by combining several smaller districts.) At the extreme, particularly small or sparsely populated school districts may not even have a high school, instead reaching an arrangement with a neighboring school district to send their students to that district's high school.