There are three ways to explain the phrase "the once and future king".
First, "the once and future king" refers to what Merlyn said to Arthur. "I will tell you something else, King, which may be a surprise for you. It will not happen for hundreds of years, but both of us are to come back." Since King Arthur had been king for one time, and he was going to come back again, he is the "once and future king".
The second explanation is from Merlyn's point of view. Merlyn came back from the future. He knew what Arthur will do and how much the impact will be as a king of Britain, then he came back to Arthur's childhood and educate him in special ways. To Merlyn, Arthur had been a king once, and Merlyn knew that little Wart was going to
