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This reaction involves addition of bromine across the double bond. The electron rich part of the double bond causes a dipole to form meaning that bromine becomes electron deficient and therefore becomes the electrophile (hence electrophillic addition). The double bond attacks the bromine and forms a new carbon – bromine bond, while the other carbon atom becomes electron deficient. The resulting carbocation reacts with the bromine ion left from the first step to form the second carbon – bromine bond.
While this mechanism is sufficient at A Level, for those looking to further study in chemistry or are interested, the more correct mechanism (via a bromonium ion) can be found