How it works
It uses 58 characters, so it is slightly less compact than Base64 but much easier to copy by hand without mistaking one character for another. “Hello” encodes to 9Ajdvzr.
Where it is used
Cryptocurrency addresses and some short identifiers, where a single wrong character would otherwise be easy to make and costly. Real addresses add a version byte and checksum on top of the encoding.
Try it
Use the Base32 and Base58 tool and read how to encode and decode Base32 and Base58.
Common misunderstanding
Base58 is not a security feature. It only changes how bytes are written as text, and anyone can decode it.