When something does not work, the first question is usually what the application actually did. Telescope answers that. It records which requests came in, which database queries they turned into, how long they took, which emails went out and where an exception occurred.
In development that saves a lot of time. Instead of forming theories, you watch the sequence. For problems that only appear under certain conditions in particular, a recording is worth more than any description.
Why it does not belong on the open internet
Exactly the property that makes Telescope useful makes it dangerous on a public server. Anyone reaching the interface sees request contents, session data and sent messages in plain text.
It becomes reachable faster than you would think, because it often gets enabled during setup and then forgotten. What else we look for is under security findings in Laravel applications.