When an individual in power approves a decision, he allows the decision to be acted on.
*The committee decided not to approve the project for various reasons. *The members of the Board approved the decision to hike the fees.
When a person in authority approves something like a building, what he is saying is that he is satisfied with it and is giving his permission for it to be used. People can move into the building. Similarly, when the Health Ministry approves a drug, what it is saying is that it is satisfied with the product and is allowing it to be sold in the market.
*The United Nations did not approve the Iraq invasion.
When you “approve of” an individual or a film, what you are saying is that you like the person/film very much.
*The minister approved of the new candidate.
Similarly, when you “approve of” something that is going to happen, you are happy or pleased that it is going to take place.
*We approve of the event taking place on the 13th.