You can get really bright LEDs now that are more than sufficient to make the clock work. Chances are that they're using some medium brightness but cheap LEDs and therefore have several of them inside the clock. You could use a single ultra bright one but they're $$$.

The LEDs provide the illumination and shine through the LCD and then the lens. Thats pretty much it. The electronics portion is a near enough a standard LCD clock but wired to light up the LEDs when you press a button.