accursed: a person or thing handed over to God for destruction and cut off forever from his people
The root idea is simple and old: something "set up" or "set apart" for God. In ordinary Greek that produced a positive word for a gift dedicated in a temple, and that gentler sense survives in the near-twin spelling (ἀνάθημα) used at Luke 21:5. But the writers of the Greek Old Testament reached for this word to translate the Hebrew idea of the ban: the irrevocable handing over of people, cities, or objects to God, normally for total destruction. Once it passed through that filter, the word kept its sense of "given over to God" but the giving now meant a sword. That is the force every New Testament use carries.
The key features all six uses share are that the surrender is to God, it is final, and it places the cursed thing entirely outside the community of the saved. This is why Paul can wish it on himself for his people's sake, pronounce it on anyone who corrupts the gospel, and even frame it as the unthinkable opposite of confessing Jesus as Lord. It is not mere disapproval or a church's discipline; it is the most severe verdict the Bible knows, transposed from the conquest of Canaan into the language of the gospel.
The shades below differ only by setting, not by core meaning. In most uses the word names the cursed state itself, declared over a person. In one use it names the binding oath a group calls down on themselves, swearing to be destroyed if they fail.