The Articles of Confederation served as the first Constitution for the United States. In an effort to avoid having a strong central government (in reaction to the strong government the colonists had experienced under Britain's rule), the original Articles were written to create the new nation as a loose conglomeration of states. They did not allow the government to collect taxes, there was no national judicial system, and there was no executive (president) to make decisions. After having gone through the Revolutionary War, the US owed money to many countries for their assistance in the war, and the lack of ability to tax made it difficult to pay these debts. Without a judicial system to decide disagreements between states, and no executive to lead the country, the young US found itself in a challenging position.
Compromises made in the Constitutional Convention included the decision of how to establish representation for citizens in Congress. There were several plans introduced, including the New Jersey Plan and the Virginia Plan, both of which benefited small states and large states, respectively. Ultimately, the Convention decided that representation would be decided based on population in the larger House of Representatives, and equally (two from each state) in the smaller Senate.
The question arose as to how to count slaves for representation purposes, because this would obviously benefit southern states more. The Convention could not agree to count them as full people, because they were largely considered to be property, so it was determined that they would be counted as 3/5ths of a person for the sake of determining population, and thus representation.