The Framers of the Constitution intended to achieve two things through the creation of federalism.
First, they intended to create a system in which the federal government would have enough power but in which the states would not need to fear the federal government. Under Britain, the central government had been too strong. Under the Articles of Confederation, it had been too weak. By creating federalism, the Framers hoped to have a central government that was just strong enough and not too strong.
Second, they intended to allow the states, with all their differences, to come together in one Union. They knew that the states were very different, with different ethnic groups, different religions, and different economic systems. They created federalism so that all these very different states could feel comfortable being tied together (somewhat loosely) in one country.