A verb meaning to unloose or loosen upon — to explain, settle a dispute, or interpret a difficult matter. The compound intensifies the basic meaning of luō (to loose) with the directive force of epi, suggesting a definitive resolution.
Mark 4:34 tells us that Jesus 'explained (epeluen) everything in private to his disciples' — the Teacher who spoke in parables to the crowds gave plain interpretation to those close to Him. This is a pattern of progressive disclosure: the mystery is announced publicly, then resolved privately for the intimate circle. The disciples who received these private explanations are the same ones who 'turned the world upside down' (Acts 17:6) — armed not with rhetorical technique but with the Lord's own epilusis of the kingdom. True understanding of Scripture comes through proximity to the Teacher, through time spent in His presence, not merely in His crowds.