PHPFreaks.com has posted part one of a series of tutorials covering some of the basics of one of the more powerful features in any language - regular expression support.
Regular expressions (which will now be referred to as "regexes") are basically pattern matching inside of text. They use special syntax and concepts in order to obtain information from a string. Many programming languages have some sort of support for regexes, because of the sheer usefulness of them. Not only can patterns be used to validate that a certain pattern exists in a string, but they can also be used to physically extract matched portions and make them usable in your PHP code.
They look at some of the basics - example structure, metacharacters, greediness as well as include a brief comparison of PCRE versus POSIX versions. The tutorial is peppered with plenty of example expressions too, giving you a good idea of what you're working towards knowing.