Typically going over one's head means one of two things (in my experience).
Option 1: to not understand something (ex: Science class was very confusing today, it was completely over my head.")
Option 2: to go to a more important or powerful person to get what you want (ex: My manager wouldn't let me work on the high profile presentation for our clients, so I went over his head and asked the company director).
Do either of those make sense with what you're reading? I'd guess the second option, based on your sentence.