This reaction proceeds via cyclic halonium ion (compare with halogenation of alkenes). However, the alternate nucleophile, water opens the halonium ion (instead of the halide ion).
Regioselectivity: X reacts as the electrophile so the C-O bond forms at the more stable cation center, or the alcohol adds to the more substituted side.
Stereoselectivity: anti since the two new sigma bonds form in separate steps on opposite alkene faces.
MECHANISM FOR REACTION OF ALKENES WITH Br2 / H2O
Same first step as for the reaction of Br2/CH2Cl2.
The π electrons act as a nucleophile, attacking the bromine, displacing a bromide ion but forming a cationic cyclic bromonium ion as an intermediate. All atoms in the bromonium maintain their octet.
Attack of the nucleophilic water molecule from the side away from the bromonium center in an SN2 like fashion opens the cyclic bromonium ion to give overall trans or antiaddition
An acid / base reaction converts the oxonium into the alcohol. The base would most likely be another molecule of water.