Vocaloids are not meant to have a story. Number one, a Vocaloid was intended to be a solution for songwriters who don't have anyone to sing their lyrics. Two, giving Vocaloids too much of a background will severely limit the creativity of producers, especially with those who tell stories through their songs. Of course, there are exceptions. Otherwise, you're probably not going to find any official background information on Vocaloids other than height, weight, and age.
However, some Vocaloids are given stories. Hiyama Kiyoteru has a band called "Ice Mountain Teru" (the band even has a site) and is an elementary school teacher. Kaai Yuki is his student. Crypton Future Media marketed Hatsune Miku as "a diva in a future where music is lost". 1st Place gave IA a basic personality as a strong and honest dreamer who wants to be friends with everyone. Tone Rion was given a brief backstory that states that shes 16 years old and was born in the year 2095 and love singing and dancing and performs on the "Dear Stage" located in the future Akihabara set 100 years in the future.