Water Puddles are environmental hazards found within the city of Columbia. They are usually the result of burst pipes or ruptured hydrants. Booker DeWitt can use the puddles (or any other body of water) to his advantage by electrifying the water with Shock Jockey, and any enemies caught in the current will incur massive, usually lethal, amounts of electrical damage. Elizabeth can also summon pools of water through Tears.
In the DLC Clash in the Clouds, a tear to a water puddle will appear after completing all challenges. Opening it will spawn a Thuggish Splicer.