The AI chat feature in Warmly allows AI to send messages to website prospects, with the sales team notified via Slack when a prospect responds. The AI sends only two messages, and the sales team continues the conversation. The purpose is to engage prospects based on filters without the sales team's active involvement, saving time and effort. Instructions for setting up Slack notifications, integrating with Warmly, and creating a default company video are provided. The importance of matching the default user with the video for a more human-like interaction is emphasized.