An academy is a fancy school, often one devoted to one subject or discipline, such as music or science. You can also use academy to describe the world of higher learning.
If you show unusual gifts as a clarinetist, you should consider attending the music academy in the next town. That's where you'll learn the most about your art. It's a private school, the Goodman Academy of Music, named after Benny Goodman, who was the greatest jazz clarinetist ever. If you want to use academy in its other sense, try "Those home experiments are cool, but without peer review, the academy will never accept them as science." Darn academy.