An evil twin is a wireless access point that is configured the same as a legitimate router in an attempt to get users to connect to the attackers router to allow for man in the middle attacks.
An evil twin is a wireless access point that is configured such that users will automatically connect to it instead of a legitimate access point for the network it is imitating. It may use physical location, signal power, or some other mechanism to try to encourage clients to connect to itself rather than its legitimate twin.
The purpose of operating an evil twin is to attempt man in the middle attacks. While it is possible to see information going over the air in an unsecure network, the negotiated session key of an encrypted wireless network makes eavesdropping and injection much more difficult (even on an open network, injection may be difficult). By getting a user to attach to an attacker controlled AP, the session is actually negotiated with the attacker, leaving the attacker free to monitor and alter traffic on the connection.
For questions related to wireless access points improperly attached to a wired network, the correct tag is rogue-ap.