A growing thing (or person) is in the process of developing, often by getting bigger. You can argue for a second helping of cake by saying, "I'm a growing kid!"
Usage Note: Grow is most often used as an intransitive verb, as in The corn grew fast or Our business has been growing steadily for 10 years. This use dates back to the Middle Ages. In the 1700s, a transitive sense arose with the meaning "to produce or cultivate," as in We grow corn in our garden.
grow /ɡrəʊ/ vb (grows, growing, grew /ɡruː/, grown /ɡrəʊn/) (of an organism or part of an organism) to increase in size or develop (hair, leaves, or other structures)