When you mix bromine with another molecule that has a carbon-carbon double bond, the bromine can add across the double bond.
The bromine atoms are very heavy - about 80 times as heavy as a hydrogen atom, or 7 times as heavy as a carbon atom. Bromination usually gives you a molecule that has higher density than the parent molecule.
Vegetable oil - which has a density of about 0.9 grams per milliliter - can be made as dense as water (i.e., 1 gram per milliliter) by adding the right amount of bromine.
Brominated vegetable oil can give an emulsion in water that is opaque and visually pleasing - it turns up in all kinds of opaque sodas and sugar/sport drinks. Is it OK to ingest bromine? Just about everyone gets away with the small amount he takes in from the occasional soda, but it's definitely possible to ingest too much - awhile back, there was a case of a person who drank as much as a gallon a day of BVO-containing soda. Turns out, he got bromine poisoning!