The loop goes from 0 to 3. Really it should go to the number of animations rather than a hard-coded number.

Here's how I would interpret the code:
Go through three images. If the position is less then the limit, draw the image and be done.
Without the break:
Go through three images. If the position is less then the limit, draw the image.

Without the break it will draw any values that satisfy the condition, and then keep going to draw any other images that also satisfy the condition.

The break is what makes it stop as soon as an image is successfully drawn.

Without the break, it was suppose to drawn the corresponding i of the animation frame but it does not show that on the game window which is weird.

So the break stops the drawing of that image once the image has been drawn?

Break steps out of the for loop.

It may be clearer to you like this:

int i = 0;
while(i < 3) {
  if(position.getY() < positionLimits) {
    break;
  }
  else {
    i++;
  }
}
g.drawImage(ghostMovementAnimation.get(i), (int)position.getX(), (int)position.getY(), null);

Oh!!! It definitely makes it so much clearer! Now I get it! Thanks so much!

Break steps out of the for loop.

It may be clearer to you like this:

int i = 0;
while(i < 3) {
  if(position.getY() < positionLimits) {
    break;
  }
  else {
    i++;
  }
}
g.drawImage(ghostMovementAnimation.get(i), (int)position.getX(), (int)position.getY(), null);

Oh!!! It definitely makes it so much clearer! Now I get it! Thanks so much! -_-