My creative writing teacher gave me a list of competitions, and one of them requires a protagonist that is transgender. What does it mean? Is it like Mulan, how she dressed up like and pretended to be a man, or does it mean people who have surgery to....you know...?

The woman who "dressed up as a man," is breaking gender-roles.

Simply put, a transgender person is someone who's gender does not match their assigned gender or sex.
(Example: Person A was assigned male at birth, but decided that their gender was not male. [This person's gender could be female, or another non-binary identity.])
A transgender person's pronouns do not have to change with their gender.
(Example: Person A decided his gender was female and his pronouns were he/him/his.)
I hope this helps future people and educated a few, too. 💖

And no surgery is needed to be transgender. That is optional.

(Yes I know this is years late)

The term "transgender" refers to individuals whose gender identity differs from the sex they were assigned at birth. It is separate from the concept of cross-dressing, which is when someone wears clothing typically associated with the opposite gender without necessarily identifying as that gender. Transgender people often go through a process called transition, which may include social, medical, or legal steps to align their gender presentation with their gender identity.

In the case of the competition you mentioned, a protagonist who is transgender would likely refer to a character who has gone through or is going through a personal journey of discovering, understanding, or expressing their transgender identity. It may involve storylines exploring their experiences, challenges, and growth related to gender identity.

To create a realistic and authentic transgender protagonist, it is important to do research and gain a deeper understanding of transgender experiences. Consider exploring articles, books, personal narratives, and speaking to transgender individuals or organizations to gather information and insights. This will help you develop a well-rounded and respectful portrayal of a transgender character.

It can apply to a variety of different persons, it is not easy to categorize. Basically, transgenders see identify themselves of differing gender categories than other people see them.

http://en.wikipedia.org/wiki/Transgender

I am not certain "pretending" is an apt description. If a man is dressed up as a woman, he may not be "pretending", at least in his viewpoint.

Your teacher is giving you a very adult topic in which you probably do not have much experience with, I suggest you discuss this with your mom to get some adult thinking input. That probably will give you some greater insight for your writing point of view.

Life's choices are not always this or that, black or white, right or wrong. Good luck in your essay.
Read this:
http://en.wikipedia.org/wiki/Transgender