to overtake or reach something that was ahead of or beyond you: to close the gap and arrive at it
At its heart this verb pictures a gap being closed. Someone or something is out in front, or out of reach, and the action of the verb is catching up to it, arriving at it, getting hold of it. The English Bible has to reach for several different words to carry that one idea, depending on what is being caught.
Most often it is a chase. A pursuer runs down the one who fled and finally lays hands on him: armies overtake a fleeing king, a master overtakes his runaway, a hunter overtakes his prey. From there the same word turns figurative: blessings or curses, troubles or guilt are pictured as pursuers that finally catch up with a person. The thing you cannot outrun reaches you.
The word also stretches to simple arrival at a target, with no chase in view. Years can reach the span of earlier years, a harvest can run right up to the next planting, a hand can reach to the mouth, a sword can reach its mark. And in the laws of Israel it settles into a fixed money idiom: when a person's hand reaches far enough, that is, when their means stretch to cover the cost, they can afford the offering. The poor person whose hand does not reach brings the cheaper sacrifice instead.
The senses below are not separate words but one motion seen in different settings: a runner catching the runner ahead, a calamity catching a fugitive, a measure reaching its mark, and a purse reaching a price.