The Linux command history is a feature that stores records of executed commands in a file, allowing for recall and reuse. To manage this history, users can clear specific entries, all history for the current session, or permanently delete the history file. Various commands are available to achieve these tasks, including `history -d`, `history -c`, and modifying configuration files like `.bashrc` to prevent saving history. Additionally, users can set variables like `HISTFILE` and `HISTSIZE` to control history behavior. By using these commands and configurations, users can maintain privacy and security when handling sensitive information.