How did political disagreement lead to important compromises in the creation of the constitution?

They disagreed on how the states would be represented. Large states wanted more representation in Congress due to their larger population, and made the Virginia Plan. Smaller states opposed with the New Jersey Plan which said all states would have one vote. 
The Great Compromise, or Connecticut Compromise, put the two plans together. Larger states would have more representation in the house of representatives and every state would have one vote in the senate.