"i=0" means assign i the value of 0.

I think i mainly gives you the x-value for the letters

The color in line 11 below is constant green.

The fading is done by lines 9+10

1.   fill(0, 10);
2.   rect(0, 0, w, h);

because the fill is black but with an opacity of only 10% so old letters slowly fade out because of this.

Here is the code to prove it with line 10 commented out:

1. int w=1000;
2. int h=w/2;
3. void setup() {
4.   size(w, h);
5.   textFont(createFont("Arial Black", 10));
6. }
7. void draw() {
8.   int i=0;
9.   fill(0, 10);
10.   //rect(0, 0, w, h);
11.   fill(0, 117, 0);
12.   while (i<w)
13.   {
14.     text((char)random(h/2), i, (frameCount*7+noise(i)*h*i)%h);
15.     i+=7;
16.   } // while
17. }