In Catholic theology incarnation means "the Word made flesh." It is God's "emptying Himself" to become a man, to suffer and die to redeem mankind. O'Connor moves her characters to work backwards from lives of evil toward a fundamental belief in the incarnation, as if they were experiencing it in its origin.
O'Connor's fiction is implicitly messaged from a believer and explicitly styled and aimed at nonbelievers. In O'Connor, we find a devout Catholic author who characterizes evangelical Protestants, an orthodox who divulges no explicit theology, a writer of Christian concerns who lampoons modern Christendom, a comic writer of the gravest themes, and a female author whose style is gender-neutral--nay, manly.
Her comic religious vision holds that a morally and socially degenerate is nonetheless spiritually a cut above the wingless chickens of privileged Christianity. She shocks her readers by beginning with divine evil as a backdoor to what is divine good so that they may rediscover what is holy, or incarnate. Her goal, I think, is to prevent her readers from taking sides among her religious forms; instead, she calls for action--from them to be seekers instead of being found.
I think what she means by the "incarnation" is that every time a christian writer becomes renowned, it is simply renowned because it brings god "back to life" and that is the only thing a christian writer can summate to is the reinstatement of faith amongst the christian audience.
For Christians "incarnation" is the belief that Jesus Christ is God. I think O'Connor meant her statement to be somewhat ironic. The phrase "God is Dead" was in common use by the early to mid 1960's and a Time Magazine cover story of that era was titled "Is God Dead ? ". Most of her writing was done before this, but it was in the air following WW II.
O'Connor meant that the people most apt to read her writing were those who were questioning organized religious belief and even the existance of God.
She thought it was "awful" that while some of her writing dealt with religious themes that her readers may have abandoned religion.