We meet Hepzibah via a memory which Dumbledore and Harry travel into via the Pensieve. She is a rich old witch who shows a young Voldemort (who, at the time of the memory, works for Borgin and Burkes) her ancient treasures and most prized possessions: Hufflepuff's cup, and Slytherin's golden locket. She is completely enamored of Voldemort, and delights in flirting with the young man.
Two days after this particular house visit, her treasures are mysteriously stolen, she is killed, and her house elf, Hokey, is blamed for the whole shebang. Knowing Voldemort's love of trinkets and trophies, and knowing Voldemort's covetous ways, Dumbledore suspects that he is both the thief and murderer.