it's based on overall click popularity - there's nothing you can do to boost it. (no, clicking on your own link a thousand times doesn't work;)
if you have a good description and your yahoo listing comes up for a lot of searches, then you eventually get to "most popular" overtime.
one tactic you can try for a couple months is to be a sponsored site in your category, to get your site listing more noticed at the top of the page if you're buried low in the listings. But that doesn't really always work, because it has to be highly visited category page, and most of Yahoo users search, not surf.
It is Click Popularity, but not totally. My site pops in and out of the "most popular" section. Sometimes I'm not there, but there is a couple sites that don't get much traffic that are there. So, it isn't just click pop.
My site is often in Yahoo's Most Popluar for my cat. Nice to get the extra link. Don't think it helps with Google PR or anything else though. Since it's near the top of the page, it may help a bit with traffic, but almost all of my Yahoo traffic comes from searches, not the directory.
I'd really like to get a pair of those cool red sunglasses though. I understand the editors give them to sites they feel warrant a visit. Funny, one of the two sites that has the glasses in my cat has not been updated since 1998, all of the email address bounce and most of their outgoing links are 404.