In short - it opens up more diving possibilities, enhances your skills, and is the next step on the learning ladder if you want to go on to become a dive professional. It's important to remember though that just because the course says "Advanced" in the title, it doesn't instantly make you an experienced diver.
Here are a few of the many options: Deep, Digital Underwater Imaging, Dive Against Debris, Dry Suit, Enriched Air Nitrox, Fish Identification, Night, Peak Performance Buoyancy, Search & rescue, Underwater Naturalist, Underwater Navigation, and Wreck Diver.