what is left of a larger whole after the rest is gone: the survivors of a people, or the remainder of a thing
She'erit names the part that is still there once most of the whole has been taken away. The picture comes from everyday loss: after a fire, a war, or a famine, you count what remains. Most often the word counts people. After an army has slaughtered or carried off a population, the few who came through alive are its remnant, and the Bible uses the word this way for foreign nations as readily as for Israel and Judah.
When the survivors in view are God's people, the word carries a hope the bare idea of leftovers does not. The prophets promise that a remnant of Israel will not merely survive the coming judgment but will be gathered back, purified, and made the seed of a renewed nation. This is the famous remnant theme of the prophets, where the smallness of what is left becomes the proof of God's mercy rather than the measure of disaster.
The same word also covers the plain leftover of a thing rather than a people. A craftsman burns part of a log and makes a god out of what is left over. The prophets speak of the rest of the nations round about, simply the others still standing. And in one old turn of phrase, to be left without name or remnant means to die with no surviving descendant, so the word can name a person's posterity, the bit of the family line that carries on.
These uses are not separate words but one idea stretched across different losses: a population, an object, a family line. What unites them is the backward look at a whole now reduced, and the question the Bible keeps pressing of whether anything has been spared.