We describe how environmental context can help determine whether oxygen (O2) detected in extrasolar planetary observations is more likely to have a biological source. Here we provide an in-depth, interdisciplinary example of O2 biosignature identification and observation, which serves as the prototype for the development of a general framework for biosignature assessment. Photosynthetically generated O2 is a potentially strong biosignature, and at high abundance, it was originally thought to be an unambiguous indicator for life. However, as a biosignature, O2 faces two major challenges: (1) it was only present at high abundance for a relatively short period of Earth's history and (2) we now know of several potential planetary mechanisms that can generate abundant O2 without life being present. Consequently, our ability to interpret both the presence and absence of O2 in an exoplanetary spectrum relies on understanding the environmental context. Here we examine the coevolution of life with the early Earth's environment to identify how the interplay of sources and sinks may have suppressed O2 release into the atmosphere for several billion years, producing a false negative for biologically generated O2. These studies suggest that planetary characteristics that may enhance false negatives should be considered when selecting targets for biosignature searches. We review the most recent knowledge of false positives for O2, planetary processes that may generate abundant atmospheric O2 without a biosphere. We provide examples of how future photometric, spectroscopic, and time-dependent observations of O2 and other aspects of the planetary environment can be used to rule out false positives and thereby increase our confidence that any observed O2 is indeed a biosignature. These insights will guide and inform the development of future exoplanet characterization missions. Key Words: Biosignatures-Oxygenic photosynthesis-Exoplanets-Planetary atmospheres. Astrobiology 18, 630-662.