We describe the simulated sky survey underlying the second data challenge (DC2) carried out in preparation for analysis of the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) by the LSST Dark Energy Science Collaboration (LSST DESC). Significant connections across multiple science domains will be a hallmark of LSST; the DC2 program represents a unique modeling effort that stresses this inter-connectivity in a way that has not been attempted before. This effort encompasses a full end-to-end approach: starting from a large N-body simulation, through setting up LSST-like observations including realistic cadences, through image simulations, and finally processing with Rubin's LSST Science Pipelines. This last step ensures that we generate data products resembling those to be delivered by the Rubin Observatory as closely as is currently possible. The simulated DC2 sky survey covers six optical bands in a wide-fast-deep (WFD) area of approximately 300 deg^2 as well as a deep drilling field (DDF) of approximately 1 deg^2. We simulate 5-years of the planned 10-year survey. The DC2 sky survey has multiple purposes. First, it serves as a realistic testbed environment for the LSST Science Pipelines. Second, the LSST DESC analysis working groups can use the dataset to develop a range of pipelines to prepare for the advent of actual data. Third, simulated data provides a controlled way to investigate systematic effects, in particular those associated with how the LSST Science Pipelines interact with the observed data. Finally, the DC2 sky survey enables the exploration of new scientific ideas in both static and time-domain cosmology.