A UUID is a 128-bit identifier designed to be unique without any central authority handing it out. That last part is the whole point. Two systems on opposite sides of the world, with no knowledge of each other, can each generate one and be confident they will not collide.
This generator produces version 4 UUIDs, which are random. Of the 128 bits, six are fixed to mark the version and variant, leaving 122 bits of randomness - roughly 5.3 undecillion possible values. The practical consequence is that you can generate them freely without worrying about duplicates.
Where the randomness comes from
The values here come from your browser's cryptographic random number generator, not from Math.random(). That distinction is worth understanding.
Math.random() is a pseudo-random generator optimised for speed. It is fine for animations and shuffling a deck for a game, but its output is predictable if you can observe enough of it. Anyone who has seen a few values can potentially work out the rest.
The cryptographic generator draws on entropy the operating system collects from genuinely unpredictable sources. Its output cannot be predicted from previous values. This matters whenever a UUID is doing more than labelling a row - a password reset link, a session token, a shareable URL that grants access to something. If the identifier can be guessed, the protection is gone.
Formats
The standard form is 36 characters: 32 hex digits in five hyphen-separated groups. This is what almost everything expects.
Uppercase is the convention in parts of the Microsoft ecosystem. UUIDs are case-insensitive in comparison, but some systems are fussy about how they are stored.
No hyphens gives 32 characters. Slightly more compact for URLs, and the format some databases use for storage.
Braces wraps the value in { }, the registry and COM format on Windows.
A note on databases
Random UUIDs make poor clustered primary keys in MySQL. InnoDB stores rows physically ordered by primary key, and because version 4 values are random, each insert lands in an arbitrary position in the index. That causes page splits and fragmentation, and the effect compounds as the table grows.
The usual answers are to keep an auto-increment key internally and expose the UUID as a separate indexed column, or to use a time-ordered identifier such as UUID v7 or ULID where the leading bits increase over time. If your table will stay small, none of this matters. If it will hold millions of rows, it matters a lot.