Mount Everest is called the world's highest mountain because it has the highest elevation above sea level. We could also say that it has the "highest altitude".

The peak of Mount Everest is 8,850 meters (29,035 feet) above sea level. No other mountain on Earth has a higher altitude. However, some mountains might be considered "taller" (with taller being "the total vertical distance between their base and their summit").

More Info: geology.com