The Public Web trigger makes a trigger available without further authentication via the Keyboard Maestro web server, which does require authentication to setup. See Set Setup and Use of Web Server.
Any macro with the Public Web trigger can be triggered by anyone without the username or password.
Public Web Trigger on a Macro
To Execute a Specific Macro
http://127.0.0.1:<Port>/action.html?macro=<YourMacroUUID>&value=<TheTriggerValueToPass> (by default, the <Port> is 4490)
As with all triggers, macros are only available if they are currently active, that is if they are enabled and in a Macro Group that is enabled and active.
For example, if you are running some sort of process on your Mac that occasionally fails, you could write a script to restart it and make it available as a Public Web triggered Macro, which you (or anyone else) could then execute to restart the process.
For a complete example with a macro, see MACRO: @Web Open URL Passed from KM Public Web Server.