Regular expressions are patterns used to match patterns of symbols in text. They allow specifying rules for what constitutes a match using special characters like brackets, pipes, periods, asterisks, and more. Regular expressions can be used in programming languages and tools like Python, Perl, Java, Excel, and more for tasks like validation and search/replace. Examples demonstrate matching strings using expressions like a(ab)*a, abc|xyz, ab+c, and a.[bc]+.