The ice in your cooler helps maintain a cold environment. The ice can't stay at a constant temperature as you use the cooler, so ice melts slowly. This melted cooler water feels very cold and it can cover food and beverages inside the cooler on all sides. Since the cold water is fluid, it gets closer to the food than the ice. As long as the cooler water is cold, it helps keep the food chilled -- and can do so more effectively than ice alone.
If the melting water will make your food soggy, do not keep the melting water in the cooler. Use the valve on the side of your cooler to drain the excess water. If you can store the food in sealable containers or bags, this lets you use the water to chill the cooler without affecting the food.
If you can't insulate the food from the cooler water, you can use refreezable ice packs or ice substitutes. These products also work well for soft coolers that could be pierced by a hard edges on ice cubes.
To extend your cooler's performance, keep it in the shade and keep it covered. Placing the cooler on top of a warm surface, in direct sunlight or in a car trunk impacts the cooling process. A large block of ice melts slower and keeps temperatures colder inside the cooler for a longer period of time. As your cooler ice melts to water, drain some of the water and add new ice to maintain an ice level inside. When all the ice melts, the cold water can slowly warm up.