They changed it so that Damien is not born of a jackal mother and is instead the son of the main character in this movie, Satan's daughter, and Satan who has taken the form of a werejackal to impregnate his own daughter. Her mother in turn is a Catholic nun who is part of a conspiracy to conceive the Anti-Christ to stop secularism and bring people back to the church.

I really hate this. Not only did we see the jackal's remains in the original (were it was a normal jackal by the way) but if the mother is half human then they missed the point. The point of the Jackal was to confirm that Damien was not human, just this mockery of a human. If he is indeed part human, then what's even the point of a jackal? We also see other demon children in the film and they don't seem like they are inherently evil either, which is just missing the point even harder. Being the son of Satan did make Damien an inherently evil monster with no hope for goodness, that's why it was dangerous to let him live.