We should also mention that the United States Senate was pretty closely modeled after the British House of Lords. Despite its royal sounding name, the Founding Fathers admired the debate format of the British Parliament. They just didn't like the ideas that came out of Parliament. How it was organized made sense to them, and when a bicameral legislature became a necessary compromise, they simply borrowed the British model.
The previous posts were very strong. I would only echo them in suggesting that the Framers were really quite afraid of a centralized government. After likening King George to the personification of a tyrant, the Framers sought to create a system where the power of one person, a central authority, would be limited by a legislative power. It is through this fear of history repeating itself that the Framers designed a Senate where each member would serve six years, outlasting the President's four. Additionally, the fear of abusive displays of power would be minimized with 100 people having power spread over their control as opposed to one or a handful.
I agree with the first answer as far as it goes, but I think that the origins of the Senate go a bit deeper than the Connecticut Compromise. To me, the Senate was "required," as you put it, because of the idea that the British form of government was too centralized and lacked checks and balances.
One of the things that the Framers most wanted to do was to create a government that would have a hard time acting on a whim. They wanted a government that could take popular passions and cool them rather than acting on them right away. They feared a government that could pass new laws easily -- they thought new laws enacted in hasted might be bad laws.
This is why they decided on a bicameral Congress. And that, to me, is why there needed to be a Senate. Once they decided to have a Senate, the Connecticut/Great Compromise was instrumental in determining how representation in the Senate would be apportioned among the states.
So, to put things more in the words of your question, what happened to require the US Senate was all the things that the British government did that convinced the Americans that it was too centralized -- that power was too concentrated in the hands of a few.
The delegates to the Constitutional Convention had a very difficult time deciding how many representatives each state would get in the new Congress. The large states felt that representation, or the number of elected officials in Congress each state gets, should be based on a state’s population (known as the Virginia Plan). They felt that states with more people deserved more representatives in Congress. Small states, on the other hand, believed that all states should be treated equally under the Constitution. They wanted all states, regardless of population, to have the same number of representatives (known as the New Jersey Plan). This caused a great deal of tension and debate between representatives from large states and small states during the Constitutional Convention. The controversy was ended with the Great Compromise. There would be a two house congress made up of the House of Representatives, where representation would be based on population, and a Senate, where there would be equal representation—every state would have two senators. The U.S. Senate was necessary to settle the dispute over representation in the new congress.