Extraterrestrial habitability is a complex notion. We briefly review what is known about the origin of life on Earth, that is, life based on carbon chemistry and water. We then discuss habitable conditions (past and present) for established life and for the survival of microorganisms. Based on these elements, we propose to use the term habitable only for conditions necessary for the origin of life, the proliferation of life, and the survival of life. Not covered by this term would be conditions necessary for prebiotic chemistry and conditions that would allow the recognition of extinct or hibernating life. Finally, we apply this concept to the potential emergence of life on Mars where suitable conditions for life to start, proliferate, and survive have been heterogeneous throughout its history. These considerations have a profound impact on the nature and distribution of eventual traces of martian life, or any precursor, and must therefore inform our search-for-life strategies.