Power refers to a person's or institution's official authority to determine what's best for others. Those in power decide how resources will be allocated among those that they rule.
Privilege allows members of a certain group to receive favors and unique benefits. It is not usually formally codified, but it exists in the fabric of our societal structure.
Power and privilege can affect us negatively or positively. For example, if you are a member of a minority in a country, you are more likely to be discriminated against, because the majority control everything and are more likely to benefit people who are like them.
The experience can only be positive if you belong to a class that has power and/or privilege. The privileged have a tendency of sticking together and supporting each other so that they don't lose their power and influence.