What is Federalism really? It's actually the opposite of a large government. It's a system where the people closest to a problem solve the problem. If you have a spill in your house, the people most capable of knowing how to remedy the problem is not a person sitting at a $1,000 desk in Washington. It is the person overlooking the spill. It's the person living in the house.
So, Federalism is a system where the communities closest to a problem solve the problem. This is why local communities do a vast majority of things. They decide where stop signs go. They decide where city parks go. They decide what rules should be in the park, and what signs should be up. They decide opening hours for parks. They decide closing hours. They decide how many workers there should be. They decide wages. When there is a problem, they solve it.
But you want your water spill cleaned up right now. So you do it yourself. That's called Federalism. It's solving most problems locally.
It's a system where the people closest to the problem directly see it, deal with it, repair it.
The founding fathers understood the importance of this. That is why they made it so hard to create a large government. They wanted the smallest government as possible. That is why the 10th amendment says, "All that is not covered in this Constitution is reserved to the states (which is the people)."
They wanted the federal government should be limited, small, and uninvolved in local events.
What is the role of the Fed, then? The Federal government is only supposed to do what the States cannot do, and the best example of this is wage war. The states cannot wage war. They can't because they would never decide what to do in a timely manner. There would be disputes. So, this is where Congress, and the President, have to make quick decisions based on the facts they have on hand.
The states also wouldn't have been able to decide on and organize an interstate highway system. So this had to be organized by the Feds. The Feds are responsible for keeping the nation safe, for securing the borders, and for creating a good economic environment where the people can prosper. That is it.
The states decide on abortion, education, healthcare, welfare, bathroom laws, etc. That's Federalism. The powers not delegated to the government is left up to the states to decide. Those who rule otherwise are "liberally" defining the Constitution and the Founding intentions.