The Linux Puppet Privilege Escalation detection rule identifies instances where Puppet commands are executed with elevated privileges, which may indicate an attempt for privilege escalation to gain root access. By analyzing process execution logs provided by Endpoint Detection and Response (EDR) agents, specifically targeting command-line interactions associated with Puppet, the rule flags any occurrences where the 'puppet apply' command is issued using sudo. This behavior is significant as it implies a user could potentially execute system commands with root privileges, raising the risk of a full system compromise. Implementing this rule ensures that organizations can detect and respond to suspicious activities that could lead to unauthorized control over their Linux systems.