PHP (recursive acronym for "PHP: Hypertext Preprocessor") is a widely-used Open Source general-purpose scripting language that is especially suited for Web development and can be embedded into HTML.
Simple answer, but what does that mean? An example:
echo "Hi, I'm a PHP script!";
Notice how this is different from a 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 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".
The best things in using PHP are that it is extremely simple for a newcomer, but offers many advanced features for a professional programmer. Don't be afraid reading the long list of PHP's features. You can jump in, in a short time, and start writing simple scripts in a few hours.
Although PHP's development is focused on server-side scripting, you can do much more with it. Read on, and see more in the What can PHP do? section, or go right to the introductory tutorial if you are only interested in web programming.