Growing is about how something becomes bigger with time. It usually refers to young living things changing into adults.
When plants grow, their seeds first soak up moisture and swell. Then a root comes out of the seed and goes into the soil. Then a shoot goes up into the air and leaves appear. These are the early, and most dramatic, changes in plants growing.
The most dramatic changes of growing in animals take place inside the mother (in mammals) or inside the egg (for other animals). Most animals come out looking like small versions of what they will look like as adults. However, insects, and amphibians are different. They will start as caterpillars (in the case of insects) and tadpoles (in the case of amphibians) and they will then change completely before they become adults.