There are vastly different answers to that question. In the most elite theaters a T.D. is primarily a
desk job and he/she is unlikely to ever even touch a piece of wood. It's about working with designers, budgeting productions, making sure the right staffing is hired, solving technical problems,
etc... there are many other people who handle the dirty work. As Marius just said, at the other extreme is Educational theater where it is often just about everything technical. In the middle there are a wide variety of other options. Unfortunately, there just is no one answer to your question.
In your case being a high school student. It means something entirely different. As you are given an amount of responsibility but you have very little real authority. There is an adult staff member who is your supervisor and has the real authority. We've had some discussions in the past about high school student technical directors. While most of us older folks were just as busy as you are now in high school and we fondly remember those days. But the truth is, what you call be a technical director has very little to do with what the position is like in the real world. Some people get a little offended by students calling themselves T.D.'s because in "the real world" it's a position that you work hard for MANY years to reach. It's earned with a lot of hard work and knowledge that would blow you away. I'm 38 and I've been the head tech person at a college for five years but it's only in the last two years that I've really felt comfortable calling myself a T.D. I just didn't feel like I had really earned that title.
I like suggesting you call yourself a Student T. D. That helps keep the confusion down a bit. Like I said I think everyone on this board has been a high school tech student and when you use the term Student T.D. we know exactly what that means, we know how hard you work and how dedicated you are to serving your school. We've all been there. At the same time it makes it clear what your position is in terms of knowledge and experience.
As for job descriptions...
When I was teaching high school I worked very hard to distribute the jobs as much as possible. In my opinion it's not good for the program or for you to have one student in charge of so many jobs. You should be trying out a wide variety of theater disciplines in high school (maybe you'll find you like running sound a lot more than designing sets, you should learn all the positions and have a chance to try them all out). I also built a mentorship system where every Jr. and Sr. had a Freshman or Sophomore working with them to learn their job. I didn't have a Student T.D. I had a team of four students who were my most trusted and skilled technicians. They met together with me and we broke down tasks into their various specialty areas and had teams handle the work.