There are many characteristics that an admissions committee will consider when reviewing your application. First, you need to show that you can do the work - this can be demonstrated by the quality of your undergraduate institution and your grades in undergrad and/or a GMAT score. Showing a history of progress and success at a brand-name firm can also show your ability to succeed (this is "proven" by promotions, raises and great letters of recommendation).
Keep in mind that plenty of candidates with good grades from top schools (and over 700 GMAT scores) are still rejected every year. In addition to "proving" that you can handle the work, you also need to demonstrate that you will be a valuable addition to a business school class (stories of professional success help here - at least 4 years of experience is good) and that you are a well-rounded person (extracurriculars/community involvement). Lastly, you need a compelling story as to WHY you want to go to business school. Surprisingly, many applicants do not convey this in their essays. They will talk about how great they are but not why they need a business degree to get to the next step/stage.
So, simply, it is a complex process for admissions committees and there are many facets that they look at in reaching their decisions. Grades and/or GMAT alone will not guarantee you a spot. Finding a school that is a good "fit" for you is important as well.
Hope this helps! I'm happy to answer more specific questions if you have them!
