The verb rend means to tear with force or violence, or into many pieces. Your parents won't be happy if your new kitten decides to rend their brand new curtains with her tiny claws.
Tear, rip, and rend are all synonyms, but it's a question of degree. Of the three, rend implies the most violent separation. You can also use rend figuratively to express great emotional distress or to describe a sharp, piercing sound. If you're betrayed by a friend, it rends your heart right out of your chest.