Zona is an organization located on the Hawaiian island of Molokai. Run by a rich and powerful man known as The Founder, that cares little for the people stuck outside in the apocalypse.
According to Doctor Merch, after the apocalypse, members of Zona created an experimental vaccine to the zombie virus. It worked at first but the vaccine started to fail and vaccinated people started turning into zombies. The leader of Zona has also been vaccinated, but now his vaccine is also failing. He is looking for a cure to avoid turning into a zombie.
After the vaccine created from Murphy's blood came with side-effects Zona's soldiers are now hunting Lucy, whom they have led Murphy to believe has died on the mainland.
Zona has a breeding program for the men and women on the island. As hinted in Season 4 episode 2 "Escape from Zona"