PHP stands for "PHP: Hypertext Preprocessor". Basically it is the language used in part to write the code for the vBulletin boards. It was developed to allow for dynamically generated web pages. Simply put it is a set of special tags that can be used with HTML tags and processed when the page is generated.
On this board we do not have the ability to post PHP code but if we did and you wanted to post a section of PHP code, if you didn't set it off using the PHP button, it would be interpreted and not displayed. It is sort of like using &lt rather than < so that the < isn't interpreted as the start of an HTML tag.