First, there's a big difference in the reputation. People who graduate from Stanford and Ivy League schools have a huge leg up over people who got their degree from other schools like Northern Arizona because of their academic reputation. Generally private schools are more prestigious than state schools, and state schools are more prestigious than for profit schools like University of Phoenix. Also, recruiters like larger schools because they can reach more applicants.

Second, the main advantage is networking and the people you meet in graduate school. If people like working with you in graduate school, they'll want to do business with you after graduation. Alumni who are hiring will give you a closer look because you have a shared background. People who get in to highly selective schools like Harvard or Stanford tend to be highly accomplished and are extra smart, show strong leadership traits, or have access to capital.