Why does the US have separate houses (House of Representatives and Senate) to form congress?
(Put another way, what is the reasoning behind a bicameral legislature in the USA?)
The U.S. Congress didn't actually start out bicameral; the original Articles of Confederation (the pre-Constitution) had a single house. The final Constitution split Congress into the House and Senate as a compromise between the large states (who naturally wanted representation to be tied to population) and the small states (who didn't want to get outvoted all day long by the larger states). Rather than pick one, they made two houses, one with representation by population and one with equal representation for each state.
The side-benefit of this split is the two houses can have completely different rules, powers, etc., and can contribute to checks and balances by watching each other. For example, only the House is allowed to pass an article of impeachment, but it's the Senate's job to actually try the impeached official. The House focuses on internal matters, particularly money, while the Senate deals with foreign policy.
More broadly, the Senate is thought to be the more mature of the houses. The minimum age is higher, and the senators serve longer terms. The House exists to serve the people as closely as possible (which is why they come from individual, relatively small districts) while the Senate exists to handle the harder, long-term issues
The House of Representatives
The purpose of the House of Representatives was to ensure adequate representation of the people to the Federal Government. This was expected to resolve the issue the rebels had with Britain not allocating representatives to the colonies, yet taxing them directly. Without a voice, the colonies had no recourse to new taxes directed to them.
The purpose of the Senate was to ensure limited government and local state power. By giving each state two representatives, no one state had any greater power over another, like was possible in the house. Additionally, by having the Senate elected by the state house rather than majority, it further secured local state power at the federal level. This of course changed with the 17th Amendment, which required Senators be elected by the populous at large.
With both houses having their various power centers, federal level representatives could not do anything without the states agreeing, and vice verse. The combination of both was supposed to limit federal power overall.
One result, perhaps unintended of the split between the Senate and the House is that they have rather different constituencies.
Each state has two Senators, and each Senator represents the whole states. They have "state" interests at heart, and up to a point, the "national" interest.
On the other hand, most states have several Congressmen, who represent "Congressional districts each representing 1/435th of the national population, or about 750,000 people. These are "local" areas, that is cities, or parts thereof (or a large rural area). But unlike Senators, Congressmen represent "local" interests.