What They Are and Whence They Came
Although more abstract versions can, and do, exist, most virtual worlds adhere to certain conventions that distinguish them from related non-real spaces. The most important of these are
The world has underlying, automated rules that enable players to effect changes to it (although not to the rules that grant them this ability). This is the world's physics.
Players represent individuals "in" the world. They may wield partial or total influence over an army, crew, or party, but there is only one game entity that represents them in the world and with which they strongly identify. This is their character. All interaction with the world and other players is channeled through characters.
Interaction with the world takes place in real time. When you do something in the world, you can expect feedback almost immediately.
The world is shared.
The world is (at least to some degree) persistent.
A chat room would not be a virtual world because it has no physics; a strategic wargame doesn't map the player onto a single character through which that player acts; a play-by-email game doesn't run in real time; a single-player game is not shared; a first-person shooter isn't persistent.
For some examples, the case is not so clear-cut. Are tabletop role-playing games virtual worlds, for example? No, because they're not automated, but it's a close call. Would a two-player educational MUD be a virtual world? Probably. Would a 500-player game with a world so vast that the players could never find each other? Yes, but under protest.
In practice, it's fairly easy to determine what is or isn't a virtual world simply by looking at its heritage. If its design draws heavily from the design of an existing virtual world, it almost certainly is one; if it doesn't, it almost certainly isn't.