An invincible, in contrast to a 1-frame throw, is a throw (and almost always a command throw) with a slow startup in return for having some invincibility attached to it.
Because the startup is slower than instant, it is possible for an opponent to evade it if they spot it in time (e.g., due to a super flash).
It is exclusively used for anti-ground stuffing. It has some difficulty of use, but if one makes careful use of the invincibility time allotted them, it can see employment as anti-air of sorts (sometimes even preferable to an anti-air throw because of this property).
In the KOF series (which probably makes the most extensive use of invincible throws), invincible throws do not start up fast enough for the opponent to stay in grab range, even from attacks with long pushback. Therefore, they will not often connect after strong attacks and command moves, but there are many cases in which they will from pokes (because the range isn’t increased as much), so they may still be usable in combos.