I think it's very important to have an idea about the strength of your application, when trying to get into a PhD program. And, to do that, one should have an idea about what schools are looking for, when evaluating an application.
If you are considering the possibility of applying to a PhD, chances are that people have been saying that you are academically great. That you are a great student, with great grades, from great schools, with great experience, things like that.
And that may all be true. I think that most people who look at my profile will think I have great chances. But, the thing is: if they had the opportunity to look at the profiles of other applicants, they would probably think most of them also have great chances.
Since the number of PhD applicants that schools accept is very limited, it is impossible that so many applicants have great chances. You may be great. But other applicants also are.
So, what schools are looking for? I'll list a few common criteria, some of them related to each other.
1 - The applicant is really interested in research. And not just interested. The applicant want and is ready to devote a whole life to research about something of his interest. If the school thinks you're interested in a PhD because you found no better job opportunities, because you have a passion to teach, because the knowledge you will acquire can get great placements in industry, or any other reason that is not to become an academic researcher, the school will probably reject you. No matter how strong you are. Ok, you may end up teaching business classes or getting a job in industry after your PhD. But those should not be the reasons to do a PhD.
2 - The applicant has at least some experience with research. The more, the better, but every little bit may help. This is not an application killer. You may be approved without previous research experience. But it helps a lot. After all, if you're so passionate about research, as you stated according to # 1 item above, you should have gone after it in some way, right? It's harder to convince someone that you are passionate about something you have never experienced before.
3 - The applicant shows a strong academic background. Your grades are great. Better yet, your grades are consistently great. Better yet, those grades are from courses that will be valuable during a PhD. Better yet, your great grades are from great schools. All schools ask for complete transcripts, and even with that some schools ask deeper questions about grades of specific types of courses.
4 - The applicant has exceptional results in the standardized tests required/accepted. Business schools usually require that applicants take either the GMAT or the GRE. I'll write more about those tests, but your scores should be at least better than the scores of 80% of the people who have taken those tests. To be competitive, your score should be better than 90%, actually. For top schools, better than 95%. Yeah, they want proof that you are the best of the best. International applicants are also usually required to take English proficiency tests, like the TOEFL or the IELST.
5 - The applicant seems to be good not only at learning something, but also at questioning something he learned. There are students who are excellent at learning existing knowledge. But a PhD requires you to create new knowledge. You cannot be a passive student, just waiting someone teaches you. You gotta be active, self-driven, autonomous, critical.
6 - The applicant has strong Letters of Recommendation. A few (usually 3) important people in academia (researchers, professors) sent letters with glowing opinions about the potential of the applicant for a PhD.
7 - The applicant fits well with the faculty/school/university. The most important aspect here is research fit. An applicant's research interests will be compared with the research interests of the faculty and the school in general. The best they can match those interests, the stronger the application. But there are other kinds of "fit" too, like the school's "personality", mission, and values, to be taken into consideration.
8 - The applicant shows an understanding about what is a PhD, and what it takes to conclude a PhD successfully. You might thing that it is taken for granted that a PhD applicant knows what a PhD is. But it seems a lot of people apply to PhD without a good idea what they are getting into. It is often said that 50% of doctoral students leave school before finishing the PhD program. One of the reasons is that students may notice they are in the wrong place during the PhD.
Of course it is extremely rare for someone to have all those qualities, and some aspects of your application may have a greater weight than others. There are also other criteria which may be used and are not listed above, like the applicant being from underrepresented minority. But the closer you are to the ideal applicant, the stronger your profile.