1: An exclamation that the other person is in fact incorrect. May only be exclaimed before correcting the other person's mistake, that is to say, when you as the speaker know how to correct the other person's mistake. In effect, the person proclaiming "incorrection" in fact proceeds to make a correction.
There are various ways that the word may be pronounced.
It may be pronounced just as it is presented phonetically in English. However, it is preferred to modify the pronunciation of the word and not speak it phonetically, and to give the word one's own unique quality.
It is highly recommended to pronounce the letter R in the word as the letter W ("incowection!").
The "tion" syllable in the word may be pronounced as though speaking French, with the "tion" being dragged out. Or the whole word may be pronounced as though it were French.
The speaker should relish every opportunity that he/she has to appropriately use the word.
2: The word may also be used pedantically when the other person is not necessarily wrong, and you are simply correcting a minor detail that the other person has made. However, this is not a very sensible use of the word and such word usage should be avoided.
Example of 1:
Person A: "2+2=5."
Person B: "Incorrection! 2+2=4. However, according to the Nazis, 2+2=5."
Example of 2:
Person A: "Documenting genocide is a bit like documenting 2+2=5. Not only is genocide morally wrong, it doesn't even make sense. It is wrong on every level."
Person B: "Incorrection! 2+2=4. Oh, now I see your point."
An attempt at correcting something already correct and making it incorrect
Jim: you spelled the word "Gigantic" wrong it should be "Jigantic"
Joe: no, you just made an incorrection
when someone corrects you, only to find that they themselves were wrong
Bill made an incorrection on my blog. He thought I spelled Hugh Hepfer wrong, but Terry corrected him yesterday.