Match Day Explained

What is Match Day?

http://www.southalabama.edu/matchday/ "This annual event, known nationwide as "Match Day", is the culmination of a process that begins in the fall when senior medical students start applying to residency programs through a national computer system. Students are then invited to interview at the discretion of each program. The NRMP has strict rules regarding communication between students and residency programs; no one can be “guaranteed” a position. Students electronically rank the programs in their order of preference and residency program directors across the country do the same.The “Match” refers to the process by which the students' and the program directors' rank lists are overlapped resulting in the selection of students for residency positions. There is also a “couples match” that strives to coordinate the match of couples to the same geographic area."

A technical explanation from the NRMP (Nat'l Residency Matching program)
http://www.nrmp.org/res_match/about_res/algorithms.html
How the Matching Algorithm Works
The NRMP matching algorithm uses the preferences expressed in the rank order lists submitted by applicants and programs to place individuals into positions. The process begins with an attempt to place an applicant into the program indicated as most preferred on that applicant's list. If the applicant cannot be matched to this first choice program, an attempt is then made to place the applicant into the second choice program, and so on, until the applicant obtains a tentative match, or all the applicant's choices have been exhausted.
An applicant can be tentatively matched to a program in this process if the program also ranks the applicant on its rank order list, and either:
the program has an unfilled position. In this case, there is room in the program to make a tentative match between the applicant and program.
the program does not have an unfilled position, but the applicant is more attractive to the program than another applicant who is already tentatively matched to the program. In this case, the applicant who is the least preferred current match in the program is removed from the program, to make room for a tentative match with the more preferred applicant.
Matches are "tentative" because an applicant who is matched to a program at one point in the matching process may be removed from the program at some later point, to make room for an applicant more preferred by the program, as described in the second case above. When an applicant is removed from a previously made tentative match, an attempt is made to re-match that applicant, starting from the top of his/her list. This process is carried out for all applicants, until each applicant has either been tentatively matched to the most preferred choice possible, or all choices submitted by the applicant have been exhausted. When all applicants have been considered, the match is complete and all tentative matches become final.

This should answer your question, Andy!