Regular expressions, or short "regex", are a pattern of characters and metacharacters that can be used for matching strings. For example, the pattern "gr[ae]y" matches both the strings "gray" and "grey".
While regular expressions are an integral part of other popular languages, they have been introduced to the Java world rather late with the release of Java 1.4 in 2002. Perl, certainly the mother language of modern regexes, already turned 15 that year.
Regexes are sometimes hard to understand, but once you got the hang of them, they will soon become your weapon of choice when you have to deal with texts.
In this article, I focus on Java code patterns for common scenarios. If you have never heard of regular expressions before, the Wikipedia article and the Pattern JavaDoc are good starting points. The Regex Crossword site is a great place for working out your regex muscles.