The boarding school book is an established genre in England. Despite the success of stand-alone U.S. novels like Curtis Sittenfeld's Prep and John Green's Looking for Alaska, there isn't really a strong tradition of books that follow a girl from her first day at boarding school until she graduates. From my perspective—and I'm not just saying this because I'm writing a series of books about a girl who goes to boarding school--that's a loss for readers and writers.
The way I see it, following a girl through her career at boarding school is an excellent opportunity for you to follow a character you like as she grows up. For the authors, it's a chance to do long-term plot and character development and planning. There is also the opportunity to create fun, short-term characters to move the plot forward and then fade into the background. Authors also often put in minor characters who don't play a big part in the series but get mentioned in a way that emphasizes the tight-knit community of a boarding school.
The plot of most boarding school books follow the progression of the path of the hero pretty closely. This is particularly apparent in the first book in a series, which is often about a new girl who is going to boarding school for the first time. The girl always has some challenges and struggles for a while. She usually descends into some kind of darkness--usually humiliation--and then emerges having conquered whatever her problem was in the first chapter.
Over the years, I've observed that there are a a number of common themes in boarding school books, regardless of when or where they are written. Often, the hero is falsely accused--and then exonerated--or the hero is misunderstood or ignored and then embraced when her peers realize their mistake. Add this to the normal emotional turmoil of being in high school and as an author, you've got a lot of material to work with.