It’s pretty much online D&D, yeah. Massive online D&D where you can do anything from do some quests alone to fight in a major player-versus-player battle of dozens of people on a side ranging across a large landscape. Hundreds of people can be on in the major “capital” cities, letting you get advice on your character’s setup or placing an order with someone to make you a particular piece of armor.
If you want, you can join a guild, which is basically a “club” of players that comes with their own personal chat channel. Some guilds just socialize in their chat channel while playing, others do casual raiding together, some are hardcore dungeon raiders that have strict participation requirements. Some are all about player-versus-player (PvP) competition with the “other side” in the game - it’s Horde (orcs, undead, tauren, trolls, blood elves) versus Alliance (humans, gnomes, dwarves, night elves, draenei).
Besides the preset private chat channel, guilds can opt to set up their own websites and Ventrilo (voice chat) servers to talk during raids or to just socialize.
Average age? No idea, probably 18ish? My husband and I belong to a casual raiding guild - people do their own thing or group up together, and we have a few 10-person raids per week, occasionally getting together with others to form 25-person raids. Our group has young teens, college students, married couples, even a grandparent or two. Plenty of women, though most are already in couples. We’re also pretty gay-friendly and have a fair number of out members in the guild. We have a voice chat server that we use for raid coordinating or socializing.
Why is it so successful? Blizzard built on their history of Warcraft games and has a pretty rich backstory that you can tease out by doing quests and listening to NPCs (non-player characters, computer-generated) talk. You can get to the top character level (currently 80, will go up to 85 at the next expansion) by never grouping with another person and doing quests/killing monsters all on your own, or you can group the entire way. You can do solo play with any character class - some are easier than others, but not overly so.
There are 5-person groups where you can fight through a little dungeon together in anywhere from 10 minutes to a couple hours, 10- and 25-person raids with massive dungeons that can take a few nights to conquer and may require strict strategies and multiple tries to finally figure out.
If monsters aren’t your thing, try your hand against smarter, faster opponents - other players. Group up with people from your “side” and fight in small or big battlegrounds to advance in level and get gear.
You can take up tradeskills (like making armor or jewelry) but don’t have to. You can auction created or found loot on a massive, automated auction house.
Explore the world! Pull off feats of daring like running naked through an enemy city and see if the guards - or opposing players - can manage to take you down! Enjoy the world’s regulary holiday celebrations. Fly on the back of a dragon and take pictures of sunsets.
Blizzard has a great mix - the game is not too hardware-intensive so lots of people can make it work on their computers. They allow user interface addons to make the interface work in all sorts of great, customized ways. They’ve got a great formula for addictiveness - constant small rewards and reachable bigger awards, opportunities to be rewarded even from short playing times, lots of variety.