Plain English Meaning
Official permission from the FCC to use the radios in an aircraft. In the U.S., you only need it when flying internationally — one license covers the aircraft's radio equipment, and a separate permit covers the pilot using it.
Full Definition
An authorization issued by the Federal Communications Commission (FCC) permitting the operation of an aircraft radio transmitter. In the United States, a Radio Station License is required for the aircraft itself when flown internationally, and a Restricted Radiotelephone Operator Permit is required for the pilot operating the radio on international flights. Neither is required for purely domestic U.S. operations.
Context Anchor
Seen when checking pilot and aircraft documents, especially before an international flight.
Derivation
Radio comes from the idea of sending signals outward, like rays spreading from a point. License comes from a Latin word meaning permission. Together, radio license means official permission to use radio equipment when the rules require that permission.