Government under the Articles of Confederation, which lasted from 1777 to 1789, was essentially a unicameral (one-house) Congress in which each state, represented by a handful of delegates, would have one vote. There was no independent executive or judiciary, though a member of Congress served as president of that body on a yearly basis. Most important, the Congress lacked the power to tax. Under this system, states had supreme power, which proved problematic after the Revolution.
The Virginia Plan, proposed by the Virginia delegation early at the Constitutional Convention, proposed to put supreme power in the national government, which would consist of a two-house Congress, in which states would be represented proportionally to their size, a strong executive and a judiciary. This is often called the "large state" plan because the representation plan benefited the more populous states. The New Jersey plan, proposed in response by William Paterson, differed from the Virginia plan in many ways, but most importantly in that it called for a unicameral legislature, where each state would have one vote, like under the Articles.
Hamilton's plan called for eliminating states altogether and consolidating them into a unified nation. The Congress would be bicameral, and both the upper house of Congress and the executive would be in office for life. It was very similar to the British model of government, and was not seriously considered.
The Constitution was the product of many compromises, but for the purposes of this question it should just be noted that it incorporates elements of both the New Jersey and Virginia plans. The process by which this happened is often called the Connecticut Compromise because Roger Sherman of that state proposed it. It includes the three familiar branches of government, but in particular it has a bicameral legislature. In the lower house, the House of Representatives, representation is determined by the population of states. In the Senate, each state is allowed two Senators.