the extra: whatever is over and above what has already been counted, whether that surplus is a leftover, an edge held over someone else, or a step too far
Hebrew has a whole family of words built on the idea of what is left over, and this is the light, flexible member of it. Underneath every use it says the same thing: there is a bit more here, beyond what has been counted. What that bit turns out to be depends entirely on the sentence around it. Left after a battle it is the livestock nobody destroyed. Set beside another person it is the edge you have on him. Pushed past its limit it is the point where being wise starts to do damage.
Eight of its nine appearances sit in two late books, and seven of those are in Ecclesiastes. That is not an accident of style. The word came into Hebrew late and went on to become one of the ordinary ways of saying "more" in the Hebrew of the rabbis, so its presence is one piece of evidence in the long argument over when Ecclesiastes was written.
Inside Ecclesiastes it does specialized work. The Teacher is auditing human life, and this is one of his measuring words: what does anyone actually have left over? He puts it as a flat question, what does the wise man have that the fool does not, and he does not answer it comfortably. Two relatives divide the same ground: the book's heavier accounting word (יִתְרוֹן) names the final balance after the whole cost is paid, and a plainer noun (יֶתֶר) names the remainder of a thing with no reckoning attached.
The last two uses are the surprise. In the book's closing paragraphs the word stops naming an extra and starts announcing one: "and besides that", "and beyond these". It has turned from a thing into a hinge in the argument, which is exactly the direction the word kept going in later Hebrew.