Ok, I'll take a shot at this.

Let's work in one dimension rather than two dimensions. It's easy enough to extend later.

You know that a any signal is the sum of a (potentially infinite) number of sine waves. For example, a square wave is the sum of ever higher-frequency (but smaller-amplitude) sine waves.

The higher frequencies are necessary to get the sharp edges.

If you strip the high frequencies, the sharp edges dissapear, leaving only the larger motions of the lower-frequency (yet bigger amplitude) waves.

So the low frequencies are the hill, and the high frequencies are the grass.

Does that make sense?

Edit: Here's an image: http://cnx.org/content/m0041/latest/fourier4.png