Why are the two rectifiers in an AC Power adapter?
Brief answer:
This is called a Switched Mode Power Supply. Mains frequency is at around 50Hz-60Hz. If you used a transformer designed for this frequency to convert your 230V to 5V, it would have to be very big and heavy.

We deal with this by increasing the frequency to several KHz, which allows us to decrease the size of the transformer for various reasons. To change the frequency like this, we first need to get rough DC, and then connect it to the input of our transformer through a switch. We then turn this switch on and off very fast (several KHz) to get the high frequency transformer input that we want. This input is then transformed to 5V, and rectified to provide a 5VDC output.