Jenny Calendar is Sunnydale's computer sciences teacher, but this is just a front for her real job, techno pagan (computer witch).
We first met Jenny when she and Willow were scanning library books onto computer, unfortunately they accidently scanned Moloch in as well and Jenny and Giles had to perform a rite to recapture him.
She does get annoyed with Giles's heightened technophobia ("Wrong and wrong, snobby. You think the realm of the mystical is limited to ancient texts and relics? That bad old science made the magic go away? The divine exists in cyberspace same as out here."('I Robot--You Jane')
Even so, she does have fuzzy feelings for Giles as well and after months of flirting they started going out. Although their first date was not quite as Giles expected, Jenny took him to a Monster truck rally
They went a a couple more dates, but it all went a little pear-shaped when Jenny was taken over by the demon Eyghon. She stayed well away from Giles and kept herself safe from harm. Deciding to apologise for her behaviour she follows Giles one night when he's patrolling and on surprising a vampire accidentally shoots Giles in the back with a crossbow bolt.
It's almost a prophecy of what's to come...
A visit by a relative of Jenny's reveals her secret, she is a member of the gypsy clan (the Kalderash) who cursed Angel after he killed one of their daughters. Jenny is living in Sunnydale to keep an eye on him and keep him away from Buffy (although she wasn't too successful there). She tells Giles and Buffy about Angel's curse, but it's a little too late for explanations now Angel has gone bad.
Buffy and Giles, stung by her betrayal cut her off totally. She tries to make amends by giving Giles a spell book with a spell to uninvite vampires. She also finishes off work on her secret project, a translation of the Spell of Restoration, the spell to give Angel his soul back.
Unfortunately, Angelus got wind of this plan (through a Drusilla vision) and tracks Jenny down in the school. She manages to save the spell on a disk as Angelus turns up and destroys the paper copy of the spell and her computer. He then chases her though the corridors of the school and when he does catch her he snaps her neck.
Angelus hasn't finished having his fun yet though. He takes Jenny's body to Giles's house and leaves it there on the bed for him to find.
Goodbye Jenny.