In my opinion, tutorial4us did a great job explaining it. A very good read indeed.
My understanding is that instance (non-static) variables exist in each object (instance of the class). Each object will have its own value/content for each instance variable. Think of the name in a Person class. We define the name as an attribute or property of a person, and each Person object will have its own name.
Static variables exist only inside the class where they are declared. Some call them "class variables" because they are bound to the class, not the object. They are unique and when a new object is instantiated, the object does not get its own copy of it. Rather than using the dot notation with the object (object.nnnn), you would use it with the class (Class.nnnn).
Note that this also applies to, and is also often used with methods!
Think about these example:
public class Test
{
public static void main (String args[])
{
int[] numbers = {1,2,3,4,5};
System.out.println( numbers.length ); // =5
// length (size/number of elements) of the array object
System.out.println( Math.PI );
// PI is stored as a static constant inside the Math class
// we don't need to instantiate a Math object to use PI
}
}