Dry flies float on the surface of the water and are usually meant to represent insects that have fallen into or are emerging from the water. Normally considered a freshwater fly, dry flies are particularly successful insects that are currently experiencing a large hatch in the area you're fishing.
In contrast to dry flies, wet flies are designed to sink below the surface of the water. Wet flies include nymphs, which imitate the immature form of insects, or streamers, which mimic baitfish and other larger aquatic prey. These flies can be very successful for catching fish that feed almost entirely underwater, like trout.