Babe - the pig in question - is the runt of his litter whose mother was taken to the slaughter house; "heaven, because every pig like it so much none has ever come back". As the runt, he was given away and used as a competition to guess the pig's weight in order to win him at a fête. Farmer Hoggett wins Babe and takes him back to the farm where he is raised by his female collie, Fly, much to the disgust of the male collie, Rex.
Babe befriends Ferdinand, a duck who wishes to be a rooster (he wants to be useful in order to avoid his inevitable slaughter). They get into trouble and, in an Animal Farm-style meeting, it is decided that Babe may no longer see Ferdinand. Babe comforts Fly and is adopted as one of her own as her puppies are given away. As Babe continues to be raised by Fly he begins to adopt the collie way of life - earning his stripes as The Sheep-Pig.
Despite this, many darker themes are hit on - the death of a bird for Christmas dinner, the death of an important character to a random attack and the constant underlying threat that Babe was only brought home for the bacon... if you'll excuse the pun. It is this that opens up the audience of Babe for those in young adulthood as well as parents and grandparents.
The animatronics in the film are very subtle - despite the animal's mouths moving to the voice overs, it is difficult to tell in which scenes fake 'animals' are used. This leads to a heightened sense of reality allowing an easily watchable film.
One problem is that the film starts of by splitting into chapters - similar to title cards in silent movies - but this slowly dies out by the midpoint in the movie. Irritatingly, the voice-overs on the chapter breaks are done by high-pitched mice whose only relevance is to just read it out. They only appear in one other scene in which they are standing around aimlessly.
Of course, this shouldn't take away from an otherwise excellent film.