You feel proud when you have a good feeling about something that you have done, or something that someone else has done. A parent may be proud of their child who has just graduated university. A child may be proud of making a very good painting.
The boy in the picture is proud of his newborn baby brother.
Something is pure if it is made up of all the one kind of thing, with nothing different. Something pure has no contaminations or anything added.
The flower in the picture is pure white.
Purebred means an animal or plant with parents of the same type, so its traits are true to its breed.
People use the term when breeding or showing animals, like dogs, cats, and horses. It is often found in pet stores, animal clubs, and pedigree papers. Some people want purebred animals for predictable features.