That looks like mold. I would discard it.
You don’t describe the process of how you made it, but if I had to make an educated guess, I would assume that you made your blackberry vinegar by combining blackberries and store-bought vinegar with 5% acetic acid? In that case, the water content of the berries can dilute the vinegar so much, that it doesn’t sufficiently suppress mold spores. Without more details, it’s hard to go into the “why” this happens, but the “what” is rather obvious.