The Virginia and New Jersey Plans were put forward at the Constitutional Convention in 1787. They were both designed, in their own unique way, to provide a workable structure for the future government of the United States. The Virginia Plan advocated the establishment of a bicameral legislature—a legislature with two chambers. The Virginia Plan also proposed that representation should be based on the population of each state. So, under this new system, Virginia, for example, would have more representatives than Delaware.
Unsurprisingly, this specific provision proved controversial. Smaller states worried that they'd be outvoted by the larger states and that their sovereignty would accordingly be compromised. It was in response to these concerns that the New Jersey Plan was put forward. Under its provisions, the new government would consist of a unicameral legislature—a legislature with only one house. Furthermore, representation in this single chamber would afford equal representation to all states, irrespective of population. The overriding concern of the New Jersey Plan was to maintain the ultimate sovereignty of the states within the American system of government.
Critics of the New Jersey Plan, such as Edmund Randolph and James Madison, argued that it would perpetuate the inherent weakness of government under the Articles of Confederation, which was no longer thought fit for purpose. The final draft of the Constitution ended up more closely resembling the Virginia Plan, establishing a bicameral legislature consisting of the House of Representatives and the Senate. Yet the approach to apportionment set out in the New Jersey Plan was enshrined in the composition of the United States Senate, in which state has two Senators, irrespective of its population size.