Dynamic nuclear polarization (DNP), a technique that significantly enhances NMR signals, is experiencing a renaissance owing to enormous methodological developments. In the heart of DNP is a polarization transfer mechanism that endows nuclei with much larger electronic spin polarization. Polarization transfer via the Overhauser effect (OE) is traditionally known to be operative only in liquids and conducting solids. Very recently, surprisingly strong OE-DNP in insulating solids has been reported, with a DNP efficiency that increases with the magnetic field strength. Here we offer an explanation for these perplexing observations using a combination of molecular dynamics and spin dynamics simulations. Our approach elucidates the underlying molecular stochastic motion, provides cross-relaxation rates, explains the observed sign of the NMR enhancement, and estimates the role of nuclear spin diffusion. The presented theoretical description opens the door for rational design of novel polarizing agents for OE-DNP in insulating solids.