Brominated vegetable oil is ordinary oil, such as olive oil, that has
had bromine added at various places to make the molecule have the density
of the sugar water in soft drinks.
This allows BVO to keep citrus and other oil-based flavorings in solution
without separating into an oil layer floating on top of the beverage.
The result is the cloudy solution you see in orange flavored or grapefruit
flavored soft drinks.
The chemical formula depicted above is that of trilinolein, a representative
component of vegetable oils. Bromine atoms would attach at various places
on the molecule to form BVO. The amount of bromine is controlled to produce
the desired density.