The Articles of Confederation was America's first constitution. This constitution was a based on colonists fear of a big central government. Keeping this in mind, it is easy to understand why the Articles of Confederation gave states a significant amount of power while the federal government had very little power. This was one of several different reasons why the US Constitution was developed to replace the Articles of Confederation.
In order to maintain a balance of power, the US Constitution created a federal government with three branches. This allows for a system of checks and balances. The judicial, executive, and legislative branches of the federal government are all limited in their power. For example, the executive branch can veto (aka override) a bill passed by the legislative branch. This veto power can stop a bill from becoming a law.