The LIKE pattern matching in MySQL checks if a string fits a pattern that can include wildcards. The '%' wildcard matches any number of characters, including none, while '_' matches exactly one character. The matching process compares the string and pattern character by character, moving forward when characters match or when '%' allows skipping characters. If the entire pattern matches the string, the row is returned. If a mismatch occurs, the row is skipped. For example, the pattern 'J%n' matches names starting with 'J' and ending with 'n', with anything in between. This is useful for searching text flexibly in databases.