The environment has something called the carrying capacity. This is the amount of life it can sustain. Limiting factors, like food, water, and light, lower the carrying capacity because there is only a limited amount available.
Overpopulation causes stress on the environment because the amount of organisms is over the carrying capacity. (To read specifically about the overpopulation of humans, see this question). This leads to a struggle for survival because the organisms are undernourished. The struggle causes damage to other organisms and the environment because of the struggle for nutrients.
Plants try to get the most soil for nutrients, crowding out other plants. Too many animals will destroy the environment around them to get more food, including different food than they usually consume, leading to struggles with other animals.
This kills off other plants and animals in the process, and the loss of biodiversity is extremely dangerous to the environment.
