The process of passing electricity through water to chemically separate it into hydrogen and oxygen is called the electrolysis of water. The balanced reaction is:
2H2O = 2H2 + O2
Electrolysis of water is the decomposition reaction of water. At normal conditions, water cannot decompose on its own. An energy is needed in order to let this reaction proceed thus it is an endothermic reaction where energy should be added in order for the reaction to happen. The energy added is the current being passed through the solution.