The meantime is the time between two events. You might be waiting for the second half of a soccer game to begin, and in the meantime call your best friend to tell her the score.
You'll most often see the word meantime in the phrase "in the meantime," and it can be used in a similar way to meanwhile. You could say, "I have to go to the store soon. In the meantime, I'm playing with the dog." This word has been around since the fourteenth century, although it was originally two separate words, mean time. Its root is the word mean, which means "middle or intermediate."