Arcology was a term coined by Paolo Soleri in the 60s and was first fully explained and delineated in the book Arcology City in the Image of Man. The book is notable because its the first comprehensive presentation of Arcology as a grand architectural manifesto for social change.
Arcology is the combination of the words architecture and ecology with the idea that architecture should be guided not purely but human creativity but also a holistic and comprehensive understanding of how the ecological systems of the planet operate so as to fully consider them when building the human built environment.
We can consider the Arcology as being a grand social theory and consisting of two main parts.
One is of the grand idea of creation starting with the big bang and then expanded out to become the universe today and the natural and interconnected order of life we see on earth. This was best expressed in the Omega Seed Hypothesis an Eschatological Hypothesis. From this notion and interpretation of creation he expresses the perspective that high density urban living is human destiny. Surburban life and its accompanying consumerism is out of sync with the essence of life.
Thus Arcology as an manifesto is the architectural will to power to recreate the city not so much as he said in his book "City in the Image of Man" but city in the image of high human values and consciousness - in balance and harmony with both human and nonhuman life. And to of course consider that higher density living may have benefits to human existence if done right. But also in that process to consider consumerism and the kind of socioeconomics that drives the life of that urban system.