Well, you hit the nail on the head when you posted this question in the biology category, because biology is the study of how organisms develop. The previous answer is almost right...if you were studying how organisms change over time you'd be looking at their evolution, but the theory of evolution in itself, via Darwin, isn't a scientific discipline on its own.
Saying you're a biologist, though, is kind of like saying you're a teacher...there are lots of different flavors. Depending on personal interests, here are some of sub-disciplines in biology:
- Biochemistry, which is interested in the chemical makeup of life,
- Molecular biology, which studies biological interactions on a molecular level,
- Cellular biology, takes a look at individual cells,
- Physiological biology studies body systems and their interactions,
- Ecology concerns itself with how organisms interact with the bigger environment.
Notice how each gets a little bigger...you start with chemicals and work your way to whole ecosystems.
Inside of biology, there are also dozens of "branches" for specialization. Here are some of the more common ones:
- Marine (ocean creepy-crawlies,)
- Pharmacology (how medicines will interact with organisms)
- Botany (plants)
- Paleontology (dinos and such)
- Zoology (animals, but not just ones in zoos.)
There are, literally, dozens more, but all of these take some interest in the development of organisms.
If you are looking specifically at literal development, you could look at embryology or developmental biology. There is also, indeed, the discipline of evolutionary biology that takes a look at how things change over time, if that is what you mean by "develop."