Answer
The reaction takes place though formation of the ring with oxygen, ring opening, and deprotonation of the product.
Work Step by Step
The following is the mechanism for the reaction:
1) MCPBA is used to form the ring with oxygen.
2) The epoxide is protonated using an acid (source of $H^+$).
3) Water attacks from the backside and opens the ring by giving the electrons between the carbon and oxygen to the oxygen.
4) Another water molecule comes and deprotonates the H on water, leaving behind an OH.
Since water can attack on any carbon attached to oxygen, enantiomers of the product can form.
