Electrolysis is the process by which ionic substances or any solution are decomposed and broken down into simpler substances when an electric current is passed through them. For electrolysis to work, the ions must be free to move. Ions are free to move when an ionic substance is dissolved in water or when melted.
Compared to pure water, milk is acidic. Infact the pH level of milk is 6 as compared to water whose pH level is 7. This is significant because each level is 10 times either more or less than the level next to it. So when comapred to pure water which is neutral, milk is ten times more acidic. Acidic mediums make better electrolytes. Hence milk conducts electricity.