An "evil twin" attack is a Wi-Fi network operated by a criminal right alongside a legitimate free, public Wi-Fi network.  The wireless network name will make it hard for you to determine it is a trap, like “hotel lobby” or “Starbucks_hi_speed.”  If you are a victim of this attack, you won’t even know anything has happened.  The rogue network will put you through to the Internet, but is now in a position to monitor and decode your messages to reveal logins and passwords.  The “evil twin” is also in a position to mount the very dangerous “man-in-the-middle” attack.

See also, What is a man-in-the-middle attack?