Ecocentrism is a belief that nature is the most important thing. The well-being of an individual person is less meaningful, through the lens of ecocentrism, than the health of the entire planet.
Ecocentrism was coined in the 1970s, modeled on anthropocentrism, the belief that humans are at the center of the universe. Eco- is from ecology, the science of living things in their environments, and centrism means "centered on." This nature-centered perspective is a relatively recent one that's held by environmentalists and some ecological philosophers. If you think nature as a whole is more important than humankind, you also see the world through a lens of ecocentrism.