animuson's answer covers the how, but not all of the why.
To quote the help pages of our network, "We're a little bit different from other sites." The system is designed to be a little worried about people who are accustomed to other sites, and may not understand what votes on Stack Exchange are intended to mean.
To prevent potentially misleading votes from skewing displayed vote counts, votes from people we don't know or users who are very new don't get recorded/shown as "real" votes. (However, as noted, they are still recorded. Sometimes they get used for analysis or fun.)
The threshold for downvotes is much higher than the one for upvotes for a few reasons. Primarily, I'd say, because downvotes are psychologically different, and in particular, can be pretty damaging/painful to recipients. Also, more practically, it's because we don't want new people blowing all their hard-earned initial rep on downvotes before they get to experience the other benefits that rep unlocks.