The phrase indicates a company or person has legal approval from an authority to do something. The restaurant was operating under licence from the health department.
Pro Tip 2/3
Validity Implication
Using 'under licence' implies that the activity is valid only for a certain period or under certain conditions. The radio station broadcasts under licence, which must be renewed every year.
Pro Tip 3/3
Exclusive Rights
Activities under licence may involve exclusive rights granted to an individual or entity. He sells the merchandise under licence, so no one else in town can sell those products.