Here are my beginning definitions of anthropocentrism, biocentrism, and ecocentrism. Later in the semester I will do a large post on each with readings that support each belief system.
Anthropocentrism is the idea that the earth and its resources exists for human consumption. People who hold this view believe that we ought to protect the earth for future generations. Anthropocentrism often focuses on fixing the problem of limited resources through the use of technology rather than a reduction in consumption.
Biocentrism views animals as important beings. Stereotypically, biocentrics are against hamrming other life forms for their own ends - many of them are vegitarians or vegans.
Ecocentrism holds that humans are only one part of the complicated system that is the earth. Ecocentrism believes tht everything has intrinsic value and emphasized the interconnectedness of all life.
The book I was reading, Green versus Gold, had a very different conception of ecocentric and anthropocentric ethics. The author, Carolyn Merchant, described three forms of ethics - egocentric, homocentric, and ecocentric. In the book, egocentric ethic was grounded in the idea that what is good for the individual is good for the society. However, with environmental issues, this is not the case, as we saw with Garret Hardin's Tragedy of the Commons. The book describes homocentric (anthropocentric) ethic as grounded in society. Homocentrism is tied to utilitarianism and the idea that the right action should maximize the good for the greatest number of people. This also often ends badly - for example, building a dam that floods a valley may produce power for a large city, but it does so at the expense of the inhabitants (human and otherwise) of the area. The third ethic described by the book is ecocentric. This ethic holds that everything (plant life, animal life, rocks, dirt, air, etc.) has intrinsic value; that is, it is good in ITSELF, not only as a means to some end. Decisions based on an ecocentric ethic take into account the whole system to be affected by the decision and therefore are more environmentally sound.
Hope this helps to clear up some of the confusion... I'll expand on all of these definitions as I continue to read and learn more!