The intermissions are descriptions from the Wikipedia article for matryoshka dolls (and Wikipedia was properly cited - Hachi asked about this on Twitter). The first just takes from the Japanese one, but the second throws in some of the alternate-language versions, too.
For anybody interested in doing a cosplay or something of that nature, the official word from Hachi on Miku and Gumi's lower halves is... "I leave it up to you." You know, I somehow knew he'd say that.
Original video: http://www.nicovideo.jp/watch/sm11809611 Lyrics: http://vgperson.com/lyrics.php?song=matryoshka