Basicly Federalism is a way of setting up a government with multiple layers so that there is more than one level that has authority over the people. Different types of government share the power associated with running a county.
In the United States our two main layers of government lie between the states and the federal aspects. Our federal system not only decentralizes our politics but also our polices. We elect leaders and representatives on a statewide level and create and vote on public policy as well.
On a national level, they give protection and establish laws for the states to follow.
The federal government also helps the states in the way of mandates. Although these mandates sometimes hurts the states instead of helping them. As congress decides to administer funds to continue programs, the states must extend the bandwidth of the program usually increasing the budget of funds needed for that particular program. This causes the states to raise more money just to receive more money from the government.
How Federalism ties in with limited government is pretty straightforward. The idea of limited government is so that there are restrictions on what the ruler can and cannot do. The multiple layer of government of federalism stays within these boundaries. The federal and state systems of governemnt perform checks and balances on one another, which insures that a law or demand will not go out unchecked.
Just having two branches of government instead of just one also insures that not one has all the power.