To sanction officially; to ratify; to confirm; to set as satisfactory.

“Although we may disagree with it, we must nevertheless approve the sentence handed down by the court-martial.”

To regard as good; to commend; to be pleased with; to think well of.

“We approve the measure of the administration, for it is an excellent decision.”

To make proof of; to demonstrate; to prove or show practically.

(English law) To make profit of; to convert to one's own profit — said especially of waste or common land appropriated by the lord of the manor.

Expressing approbation; commending

“She flashed an approving smile.”