Can you give an example of some code which you think would demonstrate
this situation?

Anyway, I was wandering if anyone in here has completed a program
similar to the one we are doing at the moment.

The program must simulate the life generation of a colony of cells,
one of our teachers said it is commonly called "Life", if anyone here
has done it, I was wandering if they'd like to upload it so I could
have a gander.

A non-static variable describes a property of a particular object, while a
static variable describe a property of the entire class. That's the whole thing
you must keep in mind.

Example: Let's imagine the class  of all pens of a given color.

public class SameColorPen
{
private static  String color = "red"; // this will be the same for all the
objects
private int size; // this will be different for all the objects

public SameColorPen(int size)
{
this.size = size;
}

public static String paint(String newColor)
{
String oldColor = color;
color = newColor;
return oldColor;
}
}

SameColorPen pen1(10); // red pen of size 10
SameColorPen pen2(20); // red pen of size 20
String oldCol = SameColorPen.paint("blue"); // this paints all the objects  of
this class in blue. pen1 and pen2 will be blue from now on.
SameColorPen pen3(30); // blue pen of size 30

Now take a closer look at the paint method  body. Inside a static method, only
static members of the class can be refered. But you are free to create and use
any other object. In the example, I declared a String object. This object  will
not be over-anything each time  the paint method is called, because it is created
and destroyed with each call, like any variable inside a block.

Yes, the object  will be overrided if you instantiate an object of another class
from a static  method, actually from all methods.
If you want it stay same over all the instances of the Class, declare a static
varible and instantiate it in the variable declaration.