I'm not sure it's a great idea to get so focused at such an early age. There's a lot to learn about the world when you're 14, and it might be good to explore a wide range of topics. (I personally took most of my "real" classes in high school, so by the time I got to college, I had an idea of what I wanted to do. After going to college for a year, I realized my needs would not be met in that way. But deciding at 20 is…
There was an entrance exam and requirements, when I attended there were four schools: Marine Academy of Science and Technology (marine-biology with a heavy NJROTC component), High Technology High School (engineering), Academy of Allied Health and Science (where I attended and focused on medical careers) and the just opened in 2000 Communications High School (video, media, design, journalism). Since graduating in 2004 they've opened a fifth, Biotechnology High School.
Though I do not have a career in medicine, I don't know anyone who attended these schools who would have traded it for anything. The academic program was one of the most rigorous in the state, and I felt truly prepared for college. The schools are consistently ranked near the very top of the US News rankings nationwide and publicly financed.
The value is in the exposure, I still have a great interest in health and use that experience frequently, I'm even an EMT which I did as a senior elective there. In fact, there's even a YC founder who went to one of our schools.
TL;DR: It's not so much specialization as it is a rigorous 4 year college prep program with exposure to a field you have interest in.