Majestic things display great dignity, befit a great ruler, or are simply far superior to everyday stuff. Compared with a peasant's hut, for instance, a king's palace is quite majestic.
The adjective majestic has origins in the Latin word majestatem, meaning "greatness, dignity, honor, or excellence." It's often used to describe things connected with kings and queens (whom, you'll remember, we often address as "Your Majesty"). We also like to refer to the great creatures and places of the natural world as majestic: Mt. Fuji in Japan for example, or a bald eagle flying over the Grand Canyon.