Base58 is a group of binary-to-text encoding schemes used to represent large integers as alphanumeric text. It is similar to Base64 but has been modified to avoid both non-alphanumeric characters and letters which might look ambiguous when printed.
Bitcoin uses a modified version of Base58 which includes a checksum. The checksum is used to detect accidental errors in the encoding process.
Bitcoin addresses are typically encoded using this scheme, which provides some error-checking features while still allowing the address to be represented in a relatively short string of text.
There are a few reasons why Bitcoin might use Base58 instead of some other encoding scheme. First, as mentioned above, Base58 includes a built-in checksum which can help detect errors in the data.
Second, Base58 strings are typically shorter than their Base64 counterparts, which can be important when dealing with large numbers (as is the case with Bitcoin addresses). Finally, the use of non-alphanumeric characters in Base58 strings makes them less likely to be accidentally typed or copied incorrectly.