A bot (robot) is a small piece of malicious code that infects a device, making it a zombie machine. The bot listens for instruction from a Command and Control (CnC) server. A group of zombies makes up a botnet (bot network) and they can all be controlled from a single CnC server to perform malicious activities.
The botnet filtering on the ASA is a license-based service from Cisco that allows the firewall to monitor, detect, and prevent such threats.