High Key means an image in which the highlights, or high tones, dominate. The "key" to the image, the most important aspect of the image (as far as tones are concerend) are the high tones, hence the name high key. Some high key images have no low tones, or no shadows.
Low key is the exact opposite. In a low key image the low tones, or the shadows, dominate the image. The "key" to this type of image are the low tones (again, in regards to tonality) hence the name low key. In some low key images there are no high tones whatsoever.