To quote the poet, 'Water,water, water, nor any drop to drink!'
Water plays its role in this reaction by 'giving' H-atoms to the diol. Arsenic posted a complete mechanism for this reaction, where you can appreciate how water 'completes' the diol.
Not only does water take part in the reaction: also OH- does it!
However, if you want to see the electrons moving, look at the arrows (every arrow is a couple of electrons)