to resolve what is unresolved: to make a puzzle plain by explaining it, or to bring a matter to a settled decision
The verb epilyo begins from a simple picture: to loosen or untie what is bound up. By New Testament times that picture had mostly worn down into two everyday uses. When the thing that is "tangled" is a puzzle, the word means to unravel it by explaining it, to make plain what was obscure. When the thing that is "tangled" is a dispute or a piece of business, the word means to resolve it, to bring it to a settled decision.
Both uses share one idea: taking something unsettled and bringing it to resolution. In Mark's Gospel, Jesus privately "explained everything" to his disciples, unraveling the parables that stayed closed to outsiders. In Acts, the town clerk of Ephesus tells the rioting crowd that any further grievance "will be settled" in the lawful assembly, not by a mob. The same verb serves both scenes because, in Greek, explaining a riddle and settling a quarrel are two ways of loosening a knot.
In the wider Greek world this was the ordinary word for solving riddles, interpreting dreams and oracles, and expounding hard texts. Jewish translators reached for it to describe what Joseph did with Pharaoh's dreams (פתר), making it the technical term for construing a hidden meaning. That background gives the Mark sense its weight: what Jesus does in private is not casual clarification but the authoritative unfolding of revelation that others cannot grasp on their own.