It essentially gives you the option to see the exception (with trace) to help you troubleshoot where the error is actually coming from. In most cases, it doesn't provide an exact location or file, but it is extremely helpful when developing or troubleshooting extension related errors such as @datitisev stated.
Edit: A real-world example would be the following that occurred in a previous version of reflar/polls
See that DEBUG
text? Clicking that text when debug mode is set to true
will bring up a modal which displays some details about the error you are encountering.
Not very helpful to the average user, but a developer can very much use that as a point of debugging their extension to provide any bug fixes in a future release.