This is actually quite a complicated topic, and I probably didn't use precisely correct language in my description. Let me try one more time:
The purpose of equipercentile equating is to equate scores between harder and easier forms of the same test. But you also have variations in the test-taking skills and abilities of different groups of test-takers. A group of MCAT takers from, say, MIT would be expected to score higher on the same test than a group from Podunk Community College. But you don't want to penalize someone for taking the test next to smart people vs. dumb people--that wouldn't be fair. So you need some way to adjust the scores to compensate for the differing abilities of the testing groups.
As a statistician would look at it, both groups are just samples from a theoretical "target population," which in this case is all applicants taking the MCAT over the course of a given year (or multiple years). The goal is to compute percentile ranks that reflect where a score would fall in this target population. The problem is that we don't know what the target pop really looks like--we have to use estimation techniques. What we want, ideally, is a way to judge how our test-taking group relates to that target population. The information a test collects to try to estimate this is called the "equating design." (I incorrectly referred to this earlier as "smoothing." Smoothing does take place in score distributions, but it's a separate process from equating.)
The MCAT uses 2 equating designs, "random groups" and "common item." "Random groups" means that people taking the test in the same place are randomly assigned one of two test forms. This gives you two groups which are both assumed to differ from the target pop by the same amount, since they are randomly selected. This allows the 2 different test forms to be equated with each other. "Common item," as I said before, uses the same questions taken by different groups of people. The peformance of a given group on the common questions is then used as a benchmark for the overall ability of the group compared to a reference standard (which, in this case, includes past MCAT takers). This allows the scores of the group to be adjusted upward or downward to approximate what they would be if they were representative of the whole target pop. THEN the percentile rankings are applied.
If you want a much better explanation of all this, look at the following document:
http://www.ets.org/Media/Research/pdf/LIVINGSTON.pdf This is an informational monograph from the Educational Testing Service about how test equating works. It is not about the MCAT per se, but it explains all the techniques used in scoring the MCAT.
