A local frat/sorority exists only on one college campus (making it 'local'). It is the only chapter of the organization, and so it does not have a national governing body or network of chapters. The chapter is responsible for itself, although often alumni aid w/ ovreseeing the chapter.
A national fraternity or sorority has several chapters on different campuses. Some may only exist on 3 or 4 campuses, while others have 100's of chapters. This network of chapters has a national governing body of some kind that oversees each chapter and maintains the GLO.
EXAMPLE:
NATIONAL: I'm a member of Phi Beta Fraternity. I was initiated in the Phi chapter. There are collegiate & alumni chapters across the nation.
LOCAL: Another GLO on my campus that I could have joined is Pi Phi Epsilon. They are the only chapter of Pi Phi Epsilon that exists
Local chapters may petition to join national GLO's if they wish, but many prefer to remain local. There are pros and cons to each situation, and I'm sure that everyone here will share w/ you their opinion