"Grow" is for plants. ( You can't grow a dog) "Raise" is for animals or a child (also "raised a family",) Breed is when you mate two animals, like dogs to make more. For example "breeders" are people who mate dogs and raise the puppies to sell. (Don't use this for people, its considered very rude)

"Grow" is like when a plant becomes big and makes fruit. "Raise" is when you take care of the plant and water it, change soil, and give it light. "Breed" is when you mate two plants to make a new plant. Of course, these are verbs, so it will work for other things than plants. Let me know if this makes sense!