Hello!
I wanted to quickly clarify before I answered that I do not know the examples from your lessons but I will do my best to conclude the answer you need.
In the United States and many other democratic republics in which power is shared between a central government and states that are called "reserved powers". Those refer to those powers that are not given to the central government, and are therefore saved or reserved for the states. An example would be a state having the power to alter its legislature.
Hope this helped :)