Federalism is the system in which (in the case of the US) the Constitution divides powers between the state governments and the federal governments. By doing this, the Constitution gives each of these levels of government their own power and prevents either level from completely dominating the other.
Under the Articles of Confederation, the states essentially had all the power to govern. The national government had no power that the states did not give it. In such a system, the power to govern is not shared.
Under the Constitution, both the federal government and the state governments have defined powers. In that way, the power to govern is shared.