I think it helps to understand what non-static means, i.e. field/methods/... that are declared without the keyword static.
Every field declared without the keyword static exists as part of an object. If you have two objects, each of these two objects has a field with possibly different contents:
class X {
int f;
}
X x1 = new X();
X x2 = new X();
x1.f = 5;
x2.f = 10;
// x1.f still is 5
However, static fields exist not per object, but per class. So in the following example, there is only one field g no matter how many (if any!) objects of class Y you have:
class Y {
static int g;
}
Y y1 = new Y();
Y y2 = new Y();
y1.g = 5;
y2.g = 10;
// y1.g is 10, because y1.g and y2.g mean the exact same thing
I personally think accesses to static fields should be made using the class (Y.g) instead of mentioning object instances (y1.g), so that the existence without any object instance is more explicit.
For methods the difference is that non-static methods are associated to an object instance, which can be accesses using this inside the method. When invoking a method declared with void m() you can access non-static (and static) fields of the object it is invoked on (so for x1.m() from the example above you can get to the field containing 5, for x2.m() you can access the field containing 10.
Static methods, however, can be invoked without having a (corresponding?) object around. If the declaration is static void n() inside class Y, you can call this method using Y.n() or y1.n() (if y1 is an instanceof Y, as above). Here, too, I prefer the first way of writing it down. Because in static methods you do not have a reference to the object instance (which is named this in non-static methods), you cannot access specific non-static fields from inside a static method - simply because there is no clear association to a specific object.
Regarding static and class definitions: This is rather advanced. You can declare a class inside another class. If the inner class is not static, every object instance of the inner class also has a reference to an instance of the outer class (which also means that you only can create an instance of the inner class if you have an instance of the outer class). This is not always what you want. By declaring the inner class static it just exists and can be used, more or less, like a class defined in its own file.
