I agree with Bmcculla.
I think gaining a full understanding of "why this component is there" or "how come a certain power supply is used" is developed through some study, experimentation and mistakes.
An approach that we have been taking in school, is to study basic circuits, such as transistor circuits, Op amps etc. We literally pick apart each minor detail to find out what is happening.
For instance, we could take a very simple 555 timer circuit (maybe a LED flasher or something) and follow the circuit through, step by step to see what voltage, amperage and what is happening at each stage in the process. This helps us understand why a capacitor is placed at a particular stage, why a resistor is placed at a certain stage, what the specific IC is doing etc etc. We usually spend 1 week just picking apart a certain circuit and analyzing the outputs. At this time, we have a pretty good idea of why everything is in the circuit, and have opened doors of opportunity to improve or add on to the circuit.
If you haven't already, I suggest analyzing the basic building blocks of electronic circuits, such as:
1. Transistor circuits
2. Op amp circuits
3. Basic timing circuits such as a 555 etc
It seems kind of boring because the circuits are so plain and simple, but the task will really open your eyes to what is really happening. Pick these circuits apart until you're blue in the face, and you can tell yourself what is happening at each stage of the process. From here you can move on to power supply analysis, etc. on up to microcontrollers.
If you would rather read up on the subject, and there is a local college nearby, I suggest going to their bookstore and purchasing an Electronic Circuit Analysis book. Though these books are pretty expensive, there is a LOT of good information for the designer to be.