JupyterLab terminals provide full support for system shells (bash, tsch, etc.) on Mac/Linux and PowerShell on Windows. You can run anything in your system shell with a terminal, including programs such as vim or emacs. The terminals run on the system where the Jupyter server is running, with the privileges of your user. Thus, if JupyterLab is installed on your local machine, the JupyterLab terminals will run there.

To open a new terminal, click the + button in the file browser and select the terminal in the new Launcher tab:

Closing a terminal tab will leave it running on the server, but you can re-open it using the Running tab in the left sidebar: