Hazel, our protagonist, has a little brother called Fiver. Fiver often has prophetic visions, and one day he has a particularly horrifying one in which he foresees the total destruction of their warren. Hazel and Fiver try to warn their leader, but he doesn't believe them. However, Hazel and Fiver form a plan to leave the warren, and after finding as many rabbits who agree to accompany them as they can (chief among them Lightning Bruiser Bigwig, a dissatisfied member of the warren's Owsla, or "officers" that assist the Chief Rabbit), that's exactly what they do.
The rabbits head across dangerous territory, rather amazingly not losing any Red Shirts en route (assuming you're reading the book and not watching the film...). They find another warren, and are invited to stay; it seems more than comfortable, and the inhabitants are pleasant and even cultured... except when they pointedly ignore simple questions. Turns out the warren does have a dark secret, and one of our heroes almost pays the price for not listening. The group beats feet, letting one of the natives come with them after he displays grief and repentance. Furthermore, since Fiver is the only one who realized the danger of that warren, his counsel on all matters is now effectively Word of God that only his brother is trusted to interpret.
Eventually they make it to a hill (the titular 'down', in UK usage) that lets them look out over the countryside, so they can always be alert to danger long before it comes near. They build a warren, acclaim Hazel as Chief Rabbit. Two of their comrades from Sandleford straggle onto the scene and relate the tragedy that befell them just after Hazel's band left. Thankful for their escape and general good fortune, the rabbits...
...suddenly realize that they didn't bring along a single female.
The tribe works out, as best as it can, a plan of action. Hazel has already made an ally out of an injured gull named Kehaar, and the bird goes off in search of other rabbits. Besides a couple of pets on a nearby farm, he finds a large, conveniently overcrowded warren nearby called Efrafa. Hazel sends a group of rabbits to attempt to befriend the other warren. In between the envoy's leaving and return, Hazel and a few others break out three of the pet rabbits. Hazel is wounded, but he manages to make it back. Unfortunately, the envoy discovers that Efrafa is the rabbit equivalent of a Fascist state, led by the monstrous General Woundwort, who isn't going to let any of his rabbits go anywhere whether they want to or not. To get the does, they're going to have to break them out.
It's beyond dangerous, but by now the Watership band is beyond desperate. Drawing on the hard lessons learned along the way, Bigwig goes undercover to infiltrate Efrafa, and with Hazel and the others as backup manages to pull off an Impossible Mission and free a group of Efrafan does. The whole tribe makes it back to the down, once again settle contentedly into peace and prosperity — only to be forced into a final showdown with the Big Bad who didn't want to let his people go.