The Botnet Blacklist is a specific threat detection used by a certain anti-malware security solution. It signals that the application has intercepted a connection over the Internet that it has determined to be suspicious enough to warrant immediate termination. As the name of the detection suggests, the identified connection carries characteristics associated with the activities of botnets.
Botnets are intrusive malware threats designed to spread over the Internet and install themselves on breached devices. Afterward, the malware net will add each infected system or smart device into a collective of so-called bots - devices that could now be exploited by the operators of the particular malware. The hijacked devices could be used for crypto-mining, launching DDoS (Distributed Denial-of-Service) attacks against chosen targets, looking for additional vulnerable devices to infect and executing other threatening actions.
The Botnet Blacklist or botnet:blacklist warning prompt is an alarming signal that should not be dismissed as a mere nuisance. However, it also is entirely possible that it was triggered in error with the AV solution flagging the activities of a perfectly genuine application. Such false positives are often caused by torrent clients or after a major software update.