UV2 flies incorporate materials that that are both fluorescent and reflective in the ultra-violet spectrum. Fish can see light in the UV spectrum that humans cannot. Ultra-violet light penetrates much further into water than visible light causing UV2 flies to be much more visible to fish than traditional flies. Shining a UV light onto these flies can give you an approximation of how fish will see them, however since we cannot see UV light directly, this is just the tip of the iceberg.
You may be wondering, if a major advantage is that UV light penetrates deeper into the water, then why would it help on dry flies? The answer is that the light reflects off of the fly and into the water, where the fish is. Since the reflected UV light penetrates better, the fly will be more visible to the fish who is looking through the water at the fly.