It is short for: "PHP Hypertext Preprocessor"... weird, but true. The PHP Hypertext Preprocessor is a programming language that allows web developers to create dynamic content that interacts with databases. PHP is basically used for developing web based software applications.
From Wikipedia: PHP originally stood for Personal Home Page. It began in 1994 as a set of Common Gateway Interface binaries written in the C programming language by the Danish/Greenlandic programmer Rasmus Lerdorf. It later versions it became known as "PHP Hypertext Preprocessor".