Jenny Calendar was a fictional character on Joss Whedon's TV series Buffy the Vampire Slayer. She was played by Robia La Morte and appeared in the show's first three seasons.
If you keep reading, you're confirming that you've either already seen the series or you don't care about spoilers.
Jenny was a computer science teacher at Sunnydale High School. She was originally a foil for Rupert Giles, the school's librarian and Buffy's watcher, though they eventually developed a romantic relationship.
The show's second season revolved around the vampire Angel's backstory, specifically the restoration of his soul (and, consequently, the ability to feel remorse) by a mystical group that wanted revenge for his killing of one of their own. In this season, Jenny is revealed to be a descendant of that group. She was sent to Sunnydale to keep tabs on Angel. There was a loophole in the curse, however; Angel would lose his soul if he ever experienced "a moment of pure happiness," which he does when he sleeps with Buffy. He promptly becomes a homicidal maniac vampire.
Buffy and her circle, including Giles, resented Jenny for not being honest with them about her identity. Eager to make amends, she begins working on a spell to restore Angel's soul, but he finds out and kills her. (Willow takes over the class; I feel like this is a thing that would not happen if a teacher's just been murdered regardless of how smart the student is, but the show's about vampires so I'm not really going to quibble with its portrayals of emergency education protocol.)
Jenny made several "posthumous" appearances, including once in season three, when evil characters took on her persona to try to get to Giles and Angel.
References
Jenny Calendar — Buffy Wiki
I finally relented and power watched all seven seasons with my husband earlier this year.