PHP (officially "PHP: Hypertext Preprocessor") is a server-side HTML-embedded scripting language.
Simple answer, but what does that mean? An example:
Notice how this is different from a CGI script written in other languages like Perl or C -- instead of writing a program with lots of commands to output HTML, you write an HTML script with a some embedded code to do something (in this case, output some text). The PHP code is enclosed in special start and end tags that allow you to jump into and out of PHP mode.