pushMatrix <-- saves the current matrix system
popMatrix <-- restores that saved matrix system

So if you want to move something in relation to the main viewpoint, do it between push and pop.

Anytime you want to move the whole thing (whole 'scene'), don't do it between push and pop.

I shouldn't have said 'matrix system'. Replace that with 'tranformation matrix'. I was putting it my own words, which is a bad idea.

Transformations are cumulative, so if I do:

translate(10,0);
translate(10,0);

Net translation afterwards is 20 in x.

If I do

pushMatrix();
translate(10,0);
translate(10,0);
popMatrix();

Net translation afterwards is 0.

Because pushMatrix saves the matrix at that point and popmatrix restores that saves matrix.

This might help explain it:

void setup () {
 size(300,300);

}

void draw () {
 background(255);

 pushMatrix();
 translate(10,0);
 fill(255);
 rect(0,0,10,10); //white square
 translate(10,0);
 fill(255,200,200);
 rect(0,0,10,10); //pink square
 popMatrix();

 fill(255,0,0);
 rect(0,0,10,10); // red square
}