What is meant by operating time of a protective relay?

Answer: The operating time of a protective relay is defined as the time which elapses between the instant when the actuating quantity exceeds the pickup value to the instant when the relay contacts close.

It simply mean that if a fault occur and current exceeds the pickup value that time really contacts get closed. The relay took very small times to close the contacts. The time between relay sense the fault to relay contacts get closed is known as operating time of a protective relay.