The concept of autopoiesis was proposed 40 years ago as a definition of a living being, with the aim of providing a unifying concept for biology. The concept has also been extended to the theory of knowledge and to different areas of the social and behavioral sciences. Given some ambiguities of the original definitions of autopoiesis, the concept has been criticized and has been interpreted in diverse and even contradictory ways, which has prevented its integration into the biological sciences where it originated. Here I present a critical review and conceptual analysis of the definition of autopoiesis, and propose a new definition that is more precise, clear, and concise than the original ones. I argue that the difficulty in understanding the term lies in its refined conceptual subtlety and not, as has been claimed by some authors, because it is a vacuous, trivial or very complex concept. I also relate the concept of autopoiesis to the concepts of closed systems, boundaries, homeostasis, self-reproduction, causal circularity, organization and multicellularity. I show that under my proposed definition the concept of a molecular autopoietic system is a good demarcation criterion of a living being, allowing its general integration into the biological sciences and enhancing its interdisciplinary use.