Hi Mary,
The game is downloaded from the Cyan servers from a link. It runs just like a boxed game, but it is a multiplayer game. Other players will be there in the 3D worlds that you can talk to, chat with, explore with, and solve puzzles with.
However, knowing that folks sometimes don't want company, each player has private instances of most of the "worlds", so you can play alone, or invite a friend (or two, or more), to your Ages (they called each location an "Age") so you can have company, but without "strangers".
I used to play in Delaware at the same time my parents were playing in Buffalo and it was fun solving the game together and chatting (you can speak with Audio also). It was a nice way to "visit", cheaper than a phone call.
As to the goal of the game, you start on an island in the clouds called Relto (your "home" in URU...even has a little hut), and you have access to only one Age, the Cleft (which is a desert in New Mexico). You have a number of steps that you must accomplish and puzzles to solve to meet those goals, all the while exploring a beautiful place. The puzzles are not difficult. When you have accomplished all of the goals, you gain access to a cave that awards you with four more Ages to explore and solve. It goes on and on.
If only for it's beautiful 3D graphics, it is worth a look.
I will post a link to the game description here when I can find it.
Hope that helps!
Dadguy
EDIT: OK, here is a detailed description (ignor the GameTap comment and the "visitor status" comments). It is long, so I suggest focusing on Introduction, and GamePlay: What Do I Do Here (there are links to these sections at the top).
http://www.guildofgreeters.com/index.php?option=com_content&task=view&id=135&Itemid=38