In many places, children are assigned to a public school based on where they live. A "school district" is an area in which all of the children are assigned to a set of public schools.
One of the factors that you have to consider when buying a house is which school district it's in.
Most cities have several school districts, some with good schools and others with schools that aren't as good. Because of this, families sometimes decide where to live based on the school district.