The Constitution acted as the backbone of the United States government after the failings of the Articles of Confederation. In an attempt to prevent the United States from being ruled by an overly powerful central government, they accidentally made it too ineffectual with their first attempt. The Constitution resolved that.
First, the Constitution established the Executive Branch of the government, which creates a central power figure and decision-making authority. It also established the three branches of government, which allowed the framers to add more power to the federal government while also being sure that it wouldn't be able to get out of control with too much power.
Second, they outright gave the federal government more power in the Constitution, delineating various rights that the states had and various powers the federal government had, which allowed them to regulate the states in certain ways while also maintaining the states's rights were not to be violated.
Finally, it established the Bill of Rights and Amendments. This section of the Constitution allowed it to be a living document to take care of issues as they arose, allowing the federal government to adapt its responsibilities and alter its power as deemed necessary by Congress.