What is federalism?

Federalism: Dividing power of government between the federal government and the states. The 10th Amendment to the Constitution gives states the right to make laws regarding anything not mentioned in the Constitution.

The founding fathers believed this was essential to preserve the individual rights of the states and to prevent the federal government from treading on state rights. This was essential to getting the Constitution passed, considering most states had differing laws regarding education, slavery, etc. 

The states were unwilling to sign a constitution that would take away these rights. Plus the founding fathers thought this was a good way to prevent the federal government from passing laws that created risky programs. Instead, it made it so a state could instigate risky programs, such as healthcare, education, abortion, etc. 

If successful, other states would copy. If not successful, other states would not copy. Likewise, if a state did something risky and failed, the other states could bail that state out. 

If, on the other hand, the federal government created a program (like healthcare, social security, etc.) and it failed, the U.S. would have to resort to another country to bail them our, or... the U.S. would fail to be a nation. 

It is to prevent such government intervention of state rights that Federalism was created by the founding fathers.