It may be that any moment is a good time to reflect on the meaning of this word, but it is particularly appropriate during the forty days that precede and include the High Holy Days. That's because the root of this word, shin-vav-bet (or, perhaps, just shin-bet), is also at the core of the main activity of the season, teshuvah, which I leave untranslated for the moment.
Of course, the "vav" at the beginning of the word is merely the conjunction "and," so we are left with "hasheiv." Its translation presents a problem in English that is not so difficult in Hebrew.
There are some action words in English that are causative as well as stative. That is, the same verb can depict the reason for an action and the action itself. Consider "stop." Compare, "if you speed, the police officer will stop you" with "when the police officer motions, I stop." There are many such words – trip, run, wave, walk, shine, to name a few more.
It is the case with "hasheiv" as well. The root means "turn" and "return," both equally. In Hebrew, this form is clearly causative, which is very hard to express concisely in English. Fortunately, we are familiar with it from the last verse in Lamentations, slightly modified in the liturgy. The juxtaposition of causative and stative make the mutually dependent nature of turning clear: hashiveinu adonai v'nashuva, "return us, God, and we shall return." The action of turning or returning requires two parties, the one who initiates and the one who completes, the one who motivates and the one who responds.
Sometimes we are both parties ("I stopped myself from crossing the line"), but more often, especially with returning, we rely on another or are relied upon by another to make the action whole. It is especially true with the process of returning and restoration. And it is especially reliable with God.