This pattern is probably one of the most simple and used pattern. As php manual says: The Singleton pattern applies to situations in which there needs to be a single instance of a class. The most common example of this is a database connection. Implementing this pattern allows a programmer to make this single instance easily accessible by many other objects.
There are tons of information about this pattern over the Internet so I let you google for it.
You can find a singleton implementation in Simple MVC framework example.