Here are some of actual use case base from my experience.
User Case #1 - debug display issue with client remotely
Say example, you are a UI developer.
Your client called you over the phone, complaint why website looks horrible (and of course, to take a screenshot is technological challenged for them) You asked them, what is the browser name (is it Chrome, FF or IE). They said, "Chrome!".
You asked back, what version. - this is where the challenge happened. Then you've asked them, are you on Mac or Windows ? They replied, "A computer.".
Well, then that the time for you to ask them to visit by saying, "at the address bar, you type adam-dot-browser-dot-beauty. After that hit Enter" (assumed that your Browser-Beauty's key is "adam").
From here, how on earth you expect them to share the screen or recite what showing on the screen ? - this is where Browser.Beauty really shine, it will send the the browser details to centre DB, and to your dashboard under key "adam".
So, basically, on your side, you login into your Browser.Beauty page, you will see your (configured) "adam" key, voila! You will see your client's UA, browser details, OS & screen information.
This is where the basic information for your troubleshooting to start.
User Case #2 - your boss's computer MUST looks pixel perfect!
As UI/UX developer, in most scenario, what your manager see, is the one that will accepted for whole-wide-world. Yeah, it is funny, but the knowledge & scope challenge for most non-IT literate manager are real. For them, what they see, is the what other people see.
So, to keep track for few bosses computer screen & browser's compatibility is important. Browser.Beauty have bookmarked feature, to add the browser's info of specific computer are saved and can easily to refer back in future.