Regular Expressions are a mean of specifying a pattern of text. For instance you can tell whether something is a valid email address by specifying a pattern like “one or more characters followed by @ followed by one or more characters”. (With RE you can write this as “.+@.+”). RE allows you to construct very complex and powerful rules for pattern matching. Whole books are written about them!
If you would like to use them in your Java programs, take a look here: