Puppies are the offspring, or children, of a mamma dog. You're the offspring of your biological parents.
This is basically another word for children. Baby horses, gorillas, lizards, and humans are all offspring. A woman who gives birth to quadruplets suddenly has a lot of offspring. But this word isn't limited to biological creations — you could say that a project you've been laboring over is your offspring. Albert Einstein's offspring included many groundbreaking theories, and the scientists who followed up on Einstein's ideas are considered his intellectual offspring.