The Andaman Sea lies off the west coast of peninsular Thailand. It is, basically, a part of the Indian Ocean that lies between Thailand and the Andaman Islands. Thailand's largest island, Phuket, is the center of tourism for the region. For divers, the most popular destinations are the Similan Island group off Phang Nga province, immediately north of Phuket. To the east of Phuket is the mainland province of Krabi, with some good diving opportunities around the Phi Phi islands.
The Andaman Sea area is huge. Unlike the more compact Gulf of Thailand diving area, where everything can pretty much be seen in a day trip from one of the main islands, you'll need to pick your specific destination, and perhaps plan on a liveaboard cruise to reach some of the more spectacular areas, which seem to be further afield.
Such is the size of the Andaman dive area that it is generally divided into three zones: The North Andaman holds the Similan and Surin Islands, as well as Richlieu Rock. South Andaman streches southeast of Phuket to the mainland, and holds such popular dive sites as the Racha and Phi Phi Islands, as well as several lesser-known sites south of Koh Lanta. Lastly, in the far south is the Tarutao Island group. Made famous by the "Survivor" television series, the waters around the smaller islands are quite good for both diving and snorkeling.