to be complete: to reach the end of something so that nothing of it is left
At its heart this verb describes something arriving at its full extent and so being done with. The same idea covers a stretch of time running out, a supply being spent down to nothing, a task being carried all the way through, and a group of people being wiped out. In each case the thing in view has been brought to its limit and there is no more of it.
Because the focus is on reaching an end, the tone of the verb depends entirely on what is ending. When days of mourning end or a building is finished, the sense is simply completion. When water, money, or strength gives out, the sense is depletion. When an army or a generation is finished off, the same verb turns grim and means perish or be destroyed.
The causative forms, where someone makes the ending happen, carry the same range: to finish a job, to use something up, or to make a full end of a people or of sin. Translators reach for many different English words here, but the underlying picture is constant: the matter has run its course to the last.