Question: The school I'm applying to requires three letters of recommendation and the application says that it accepts "professional recommendations?" What does that mean?
It means that the program will accept letters from people who have supervised you or worked with you in non-academic settings -- jobs, internships, or volunteer work. In other words, the program will accept recommendation letters that are not written by faculty.
Given that graduate school is an academic endeavor, ideally your letters of recommendation would come from people who know you within an academic context. Professors you've taken in class, who you have worked alongside as assistants, who have supervised your research or who have mentored you are the best source of effective letters of recommendation. Some applicants, however, do not have three faculty to turn to because they have been out of school for a while, are changing fields, or for other reasons. The program to which you are applying recognizes this. Learn more about what to do about getting a letter of recommendation when you're changing careers as well as how to select persons to write on your behalf.