After the showing of the third and final OAV of 3x3 Eyes II: Legend of the Divine Demon, the most common comment I heard was "Uh... so what happened?"
Like most anime, both series of 3x3 Eyes are based on a manga series, specifically volumes 1-5 (the manga series is currently well on its way to a 23rd tankoubun). When trying to tell that much of a story in so short a time, a certain compression factor sets in, and certain things are left out. Although 3x3 Eyes is nowhere near as guilty in that respect as Please Save My Earth, a lot of information was squeezed into the end of the last episode. Knowing some of the information from the manga (the first 5 tankoubun, and some later ones as well) helps clear up a lot about the series.
The Sanjiyan with a split personality. Pai is the cheerful and naive main personality, and Pavarati IV is the arrogant Sanjiyan personality. When Pavarati is in control, the voice shifts and the third eye opens. Yakumo refers to this personality as Sanjiyan.
Pai never actually shows up in 3x3 Eyes series II. The main personality in this series was actually Howasyou without her memory, although she thought she was Pai and was called that. Pavarati first manifests in the second episode, sans memory and very, very upset.
It's revealed later in the manga that all of the Sanjiyan either developed a similar personality split or went insane in other ways.
A demon snake who was used by Benares to perform Choang-Lin-Lin on Pai, sealing off her memory and personalities. Her physical body was transformed into the rhombus on Pai's forehead (her "scar"), and she took control of Pai's body. In the process of the Choang-Lin-Lin, Howasyou lost her memory and thought that she was Pai (Yakumo thought so too).
After Howasyou left Pai's body in the confrontation in the holy land, Pavarati, for reasons unknown (gratitude? Nah...) gave Howasyou her own human body and reinserted her in Ayanokouji Pai's life, with only a slight memory wipe. Howasyou shows up again later in the manga.
The "glove" Yakumo gave Ayanokouji Pai. It allows a personality to call out the Sanjiyan's power without calling out the Sanjiyan personality when the proper spell is recited.
Of course, there's much more left to tell in the story, like re-awakening the Pai personality fully (the reason why Pavarati was leaving Yakumo at the end of the last episode), getting back to the Ningen no Zou and figuring out how it turns Sanjiyans into humans, the Hyouma tribe, culinary school (culinary school?)...
If you liked this series, there are a few English translations of the manga, as well as the 17 (and counting) tankoubun to go in Japanese, and there is even a 3x3 Eyes TV series in production in Japan right now.