Permanent markers were designed to withstand rain, sleet and snow as the ink is intentionally not water-soluble. Over time, water and sunlight may leech some of the ink's color and cause it to fade, but that can take years and will likely not fully remove the ink. Water can smear the ink if applied immediately after you write something with a permanent marker. Wet surfaces can prevent a permanent marker from leaving as strong a mark unless the pen was made to be used in wet conditions.
Dipping a permanent marker's tip in water for a short period of time will not have much of a long-lasting effect; it will likely not write well until the water has evaporated or been transferred to another surface. Leaving a marker with its cap on in water will likely not damage it since the seal is tight, but soaking a marker in water without a cap often ruins it as the water mixes with the ink inside the pen.
Water is often the first substance used to prepare an ink-stained surface for another chemical that will remove it. Dabbing water on a fabric and then applying a light spritz of hair spray followed with a few drops of white vinegar will get many stains out. After letting the chemicals sit, the stain is then flushed out with water. Water can also be combined with toothpaste or baking soda to remove the ink.
Rubbing alcohol can be used to repair a permanent marker with a dried-out tip. Nail polish remover and denatured alcohol will both often remove these ink stains when used separately. Some store-bought products are designed to specifically remove marker stains and are often available in the cleaning section of grocery stores.