Moiré can occur in the resizing of an image when patterns in the original image create new patterns in the derivative image. For an example, let's take this image, a series of lines:
Let's say we want to resize this image by 25 percent (in terms of area). Obviously, to do so, we must delete 3 out of every 4 pixels. To visualize this, pixels that are going to be deleted have been marked in red. Here, the top left portion of the image has been marked for resizing:
And now the whole image, marked for resizing:
Now let's remove those red pixels and collapse the image:
The lines have changed directions! Because lines in real photographs are rarely perfectly straight and parallel, the resulting lines (as in the last image) are often curved, but the result is the same: a Moiré pattern.