Under the Articles of Confederation, the central government could:
1) Declare war on another country.
2) Raise an army.
3) Develop treaties with other countries.
4) Can allow new states to join the US with a 9/13 vote.
Besides the aforementioned responsibilities, the central government was very limited in what actions they can take. State governments could actually ignore the laws made by the central government if they felt they were unjust. This is one of the main reasons why the Articles of Confederation only lasts for about a decade in America.