The Match is where all the medical students across the country, after rotating and interviewing at desired programs, rank those programs. Basically like a top ten list, some rank more some less. The residency programs do this as well, rank the candidates. Then on a certain date, AOA is in Jan (i think someone else can correct me) and the ACGME is in March. This is called Match Day, when all those students find out where they are going to do their residency. It is decided by feeding all the rankings from students and programs in a computer system. This system then matches your closest top match with the programs that ranked you the highest, basically matching those that desire each other, ie if you ranked a program number one, and they ranked you number one, that is where you are going.
The reason people post schools ranks is for two reasons. One is some people think that it is predictive of how good the school is, or more specifically what kind of programs they may be able to get into if they got to that school. The other reason is say you want to go to Big City hospital to do your residency, and your school has a few students that have gone there, you now have some leverage to gain a position there by having access to those residents, and you know that that program is familiar with your school.
I tend to disagree with the first part, it lends some value but just remember that YOU are the one in school, not last years fourth years. Classes can vary by how well they do. Some classes are very good some F#$% off and don't study. Pick a school that one is CHEAP and fits your needs.