Zarkon is the evil ruler of the Galra Empire, and it is his mission to not only take over the universe, but to have the power of Voltron in his hands.
It was Zarkon who first started this galactic war nearly 10,000 years ago. Which should have been impossible, however, likely through the power of quintessence, he has extended his life to near immortality, and has continued to rule with an iron fist.
Zarkon believes in "survival of the fittest" and actively seeks to find the strongest beings in the universe. Even putting on gladiator matches to see how prisoners do in battle.
In the final episode of Voltron Legendary Defender season 01, Zarkon reveals that he was the first Paladin of the Black Lion, even still possessing the weapon associated with the Knight. It's unclear how he lost that title, but it revealed why he wanted Voltron so much, and how he knew so much about the Alteans and of Voltron.
With a force that spans the galaxy, Zarkon is truly a villain worthy of Team Voltron.