Usually it's more difficult to actually find a job as a gardener than it is to qualify for it. While the specifics all depend on the job and the pay—for instance, you should probably know something about cacti and succulents if you're going to be helping to remodel a desert oasis—the average gardener just needs to be proficient in yard work.
Mowing the lawn and raking the leaves are basic tasks, but it still takes a certain knowledge and work ethic to get the job done in a good amount of time.
A more thorough education is an asset for upper-level jobs. Without a high school diploma or GED, you're less likely to get a position as a supervisor or manager.
Larger landscape companies need someone with a Qualified Applicators License in order to apply pesticides, and that takes some learning to earn (source). Qualified irrigation technicians and arborists have their uses, and those roles usually require a college degree.