The Bandersnatch was an experimental B.O.W. (Bio-Organic Weapon) created using the
t-Virus which was intended to act as a 'base' body for future Tyrant projects. Many were produced en masse and was not intended to be active without further modifications to it's physiology so any that were caught in the wild were considered escaped and had to be destroyed.
The name comes from Lewis Carroll's poem Jabberwocky which is part of the novel Through the Looking Glass and also appears in his later poem The Hunting of the Snark. The name given to the B.O.W. doesn't appear to have any real relevance to the source material so it may be that an Umbrella staffer who named the creature was simply a fan of Caroll's work.
They were developed on a tight budget to attempt to counter the extremely high costs involved in developing a single successful Tyrant. Unfortunately due to the lack of time and research into their development they tended to lose their effectiveness after a short time - most commonly was that their left arms atrophied to the point where almost the entire limb re-absorbed into the body and only a tiny appendage was left, as well as their legs which meant that they stumbled around from being so top-heavy.
One of the main advantages of the Bandersnatch was it's right arm which was enormous compared to the rest of it's body, including the fact that their extremities had the ability to stretch in order to reach a far away target.
A number of Bandersnatch prototypes were stored on Rockfort Island where Umbrella were intending to use them to gain combat data against prisoners which they held on the island. However, the H.C.F. led by
Albert Wesker subsequently raided the island and took the combat data for himself, leading him and his organisation to develop an enhanced version of the B.O.W. named the
Jabberwock S3 which used the more dangerous t-Veronica virus as a base but still shared many of the original models advantages and disadvantages, but was ultimately scrapped as well.
No additional creatures were ever developed using the Bandersnatch research, with Umbrella deciding to go down other routes for future Tyrant projects such as Parasites or simply going back to the drawing board with the
t-Virus.