From Academic Kids
In countries with federal systems of government, and subnational entities offically called (or widely-known as) states, a state government is the governing body of a state. State governments share power with a federal government or national government. Some state governments may be deemed to have limited sovereignty, whereas others are subject to the direct control of the central government.
Under the 10th Amendment to the U.S. Constitution, all governmental powers not granted to the United States Federal Government by the Constitution are reserved for the states. The governments of the 13 colonies which formed the original union under the Constitution trace their history back to the royal charters which established them during the era of colonialism. Most other states were organized as federal territories before forming their own governments and requesting admittance into the union. Notable exceptions are Vermont, Texas and Hawaii, which were sovereign nations before joining the union.
All U.S. states have a written constitution and a three-branch government modeled on the U.S. federal government, although this particular structure is not mandatory.
The legislative branch is typically a bicameral legislature. (Nebraska has a unicameral legislature.) The upper house of state legislatures is usually called the senate and the lower house is usually called the house of representatives. (The lower houses of New York and California are called the Assembly. Connecticut's house and senate together are called the General Assembly, and the bicameral legislature of Massachusetts is called the General Court.)
The judicial branch is typically headed by a supreme court which hears appeals from lower state courts. The structure of courts and the methods by which judges are elected or appointed is a determined by legislation or the state constitution. (New York's highest court is called the Court of Appeals.)