What problem does this solve, or put another way, what is our motivation to use it? In nearly every application, there is a need to have an area from which to globally access and maintain some type of data. There are also cases in object-oriented (OO) systems where there should be only one class, or a predefined number of instances of a class, running at any given time. For example, when a class is being used to maintain an incremental counter, the simple counter class needs to keep track of an integer value that is being used in multiple areas of an application. The class needs to be able to increment this counter as well as return the current value. For this situation, the desired class behavior would be to have exactly one instance of a class that maintains the integer and nothing more.
At first glance, one might be tempted to create an instance of a counter class as a just a static global variable. This is a common technique but really only solves part of the problem; it solves the problem of global accessibility, but does nothing to ensure that there is only one instance of the class running at any given time.
Not quite: the static global variable will be one instance of the class, but maybe by accident or mistaken intention one might create another instance of the class other than that static global variable.