For the first decade of American existence, the nation wasn't really a cohesive, single entity. Rather, it was a loose group of states that fought Britain in the American Revolutionary War. This was known as the Articles of Confederation, and the Articles were a framework for an extremely small, limited central government that was meant as a reaction to the tyrannical government in Britain that the colonists had broken away from.

The Articles were a mess. During the revolution, the Articles government was unable to accomplish simple wartime tasks due to foundational flaws. The final straw on the camel's back was Shays' Rebellion, which was a backlash from Continental Army soldiers who had never received their pay. Due to this, the Articles were scrapped and a Constitutional Convention was called to create a new government.

When it came to deciding the structure of a legislative branch of government, there were, essentially, two competing plans of action.

First was the Virginia Plan. This called for proportional representation within Congress, in order to represent the people within states, not the states themselves. This sounds fine, but then you realize that the Virginia Plan was made by wealthy Southern white landowners for wealthy Southern white landowners, as the Virginia Plan favored states with high populations, such as Virginia.

In opposition to the Virginia Plan was the New Jersey Plan, which wanted smaller states to be represented equally through state representation, wherein each state would get an equal amount of political power.

These two plans both had their merits and their flaws, and neither side was willing to back down. So the Great Compromise (alt. the Connecticut Compromise) was made. The Great Compromise decided to create a bicameral (two house) legislature modeled after Great Britain's, where there would be a lower house and an upper house, akin to the House of Commons and the House of Lords. The lower House of Representatives would practice proportional representation, while the upper Senate would practice state representation. This way, both sides would be happy. And both sides were.

Congress has changed a lot throughout the years. In particular, the Seventeenth Amendment of 1913 changed the method in which senators were chosen. Previously, it had been by vote of state legislatures, but the Seventeenth Amendment changed this to a direct vote.

Obviously, this is a very quick look into the reason behind the bicameral legislature of the United States, and I recommend that you look into it more, because there's a lot that I'm not covering.