The 16X PWM board is basically a bunch of mosfets under PWM control (switches that turn on and off really fast) that can be used to mix different levels of the main three DIODER colors: red, green and blue. The PWM board also has a bunch of fading and sequencing commands built in, so the arduino code is fairly simple.
The 16X board could also be controlled from a serial port, but adding the arduino provides a lot more capability, like being able to control the lights based on a pot input, or maybe a color sensor to emulate ambient lighting...
Here's a video showing a quick demo:
Somebody on youtube asked how the LED strip electrical circuit, so here are some details if you'd like to use completely different electronics to control the Dioder, or many other LED strips.
Most of these strips are made to accept 12V, no matter how long the strip is. The LEDs are arranged into groups of 3, and the strip can be cut between each group. Electrically, each group is wired in parallel. So whether you have 1 group, or 100, you always supply 12V. Each additional group requires more current and power.
In this particular LED strip (the DIODER), the red channel consumes .14A, blue .11A and green .13A. So all together, the strip requires a max of .38A at 12V, or about 4.5W. If you look on the power brick, it says 5W max. The strip is about 33in long, and has 12 groups of LEDs, so each group requires 31mA of current, and .37W of power. If you added another strip on the end, you would need about 9W of power, and .76A of current, but still 12V to drive the whole thing.
This arrangement makes it very easy to fade the LEDs by varying the voltage with PWM switching. Even if the total length changes, the fading circuitry stays the same as long as it can handle the additional current.