Furthermore, it opens a back door and connects to a command and control (C&C) server, which allows the remote attacker access to the compromised computer. The attacker is then able to perform any number of actions on the computer, and the computer may then become part of a wider botnet.
This is why I am concerned. If this was nuisance malware, I would clean up and wait. If my computer is now part of a botnet, I'm not so sure I would see obvious activity.