To bring an unsettled thing to a settled state. Also to turn a reference into the thing it points at.
Latin resolvere (to loosen, to untie, to dissolve): re- (again) + solvere (to loosen); to resolve is to untie an unsettled thing into a settled one, or to untie a reference into the thing it was always pointing at.
To bring an unsettled thing to a settled state, or to turn a reference into the thing it points at. The root's untying covers both: something knotted is loosened until it is plain.