Understanding the ionic diffusion mechanism in polymer electrolytes is critical to the development of advanced lithium-ion batteries. We report here molecular dynamics-based characterization of structures and diffusion in poly(ethylene oxide) (PEO) with lithium and bis(trifluoromethysulfonyl)imide (TFSI) ions imbedded into the PEO structure. We consider a range of temperatures (360-480 K), molecular weights (43, 22, 10, and 2 chains with 23, 45, 100, and 450 EO monomers, respectively), and ion concentrations (r = 0.02, 0.04, 0.06, and 0.08 Li:EO) for which there is experimental data. The found dependence of the diffusion coefficients on these variables is in good agreement with experimental measurements. We then analyze how the diffusion performance depends on details of the atomistic diffusion mechanism, the motion of the Li and TFSI along the polymer chains and hopping between them, the role of polymer motion, the temperature dependence of the intrachain and interchain diffusion contributions to the total ionic diffusion coefficients, and how these depend on ionic concentration and molecular weight. The most diffusive Li atoms exhibit frequent interchain hopping, whereas the least diffusive Li atoms oscillate or "shift" between two or more polymer chains. These shifts may affect the segmental motion of the PEO-LiTFSI polymer that is expected to be important for fast lithium-ion diffusion. The excellent agreement between experiment and theory validates the approach and methodology used in this study, setting the stage for applying this methodology to predicting how to modify the polymer structure to increase ionic conductivity for a new generation of electrochemical materials.