The Great Compromise is also known as the Connecticut Compromise. It was a compromise over the nature of the US Congress. The compromise was reached during the Constitutional Convention of 1787.
When the Constitution was being written, there was a dispute between the big states and the small states. The big states wanted Congress to be apportioned by population. They wanted states with more people to have more representatives in Congress. By contrast, the small states felt this was not fair. They thought that all states are equal and that all states should, therefore, have the same number of representatives in Congress. This was the cause of some conflict.
The Connecticut Compromise/Great Compromise solved this problem. First, it created a bicameral Congress (one with two houses). Then, it apportioned one house according to each of these methods. The House of Representatives would be apportioned by population. That is why California today has more than 20 times more representatives than Wyoming does. The Senate by contrast, was to be equal. That is why each state has two senators today.