Plants are necessary because they are a primary food source and provide the oxygen that is vital to animals' and humans' existence. A majority of the calories that people consume comes from plants, and most meat comes from animals that eat plants. Plants are at the bottom of the food chain, and animals could not survive without them. Plants also release the oxygen that humans and animals breathe.
If all plant life disappeared, animals would die quickly. Most animals eat plants, and most carnivores eat animals that eat plants. Animals have no means of creating the fuel they need without food, and the only remaining life on earth would be single-celled organisms. Even some bacteria would die, as many depend on plant cells to survive.
Plants also create the oxygen animals need to survive, and it was algae that created the oxygen-rich atmosphere animals need. While it would take a long period of time for oxygen levels to drop to dangerous levels if plants did not exist, the change would be inevitable. Plants also consume harmful carbon dioxide.
Not all plants survive on land, and ocean ecosystems would be wrecked as well without plants. As with life on land, life in the sea depends on a food chain with plant life near the bottom. Plants in the ocean are responsible for generating most of the oxygen in the atmosphere. Because of this, high levels of acidity in the ocean could eventually cause a significant amount of atmospheric harm.