Landmarks are locations on the Map you can fight over and control with your Community. The Community that controls a Landmark will gain rewards and benefits while they control it. You will start to target Landmarks when you reach mid-game, starting with smaller ones such as police stations and clinics which will offer large amounts of a single type of supply to scavenge.
Eventually you will start to look toward the bigger more famous Landmarks from the Walking Dead series such as Alexandria, The Hilltop, The Kingdom, and Sanctuary where you will recieve big rewards for winning and controlling them. Although the rewards are substantial for taking over one of these big Landmarks they also come with a lot more risks.