This Arduino power supply is designed to "do the right thing" no matter which source of power is plugged in.
the right thing
"The right thing" is:
- When a person plugs in only the USB cable, the CPU and everything else powered by the +5V line is powered from the +5V USB power.
- When a person correctly plugs in only a 12 V wall-wart, the CPU and everything else powered by the +5V line is powered from a +5V voltage regulator powered by the wall-wart.
- When a person correctly plugs in both the USB cable and the wall-wart are plugged in at the same time, all the power comes from the wall-wart, and no power "back-flows" to the USB host.
- When a person keeps plugging and unplugging the cables, the power smoothly transitions from one to the other, so that as long as at least one is plugged in correctly at all times, the CPU continues to run uninterrupted.
- When (not "If" !) a person plugs in a 12 V wall-wart incorrectly -- reverse polarity -- no current flows to or from the wall-wart, no damage is done, and the system acts exactly the same as if that wall-wart isn't plugged in at all.
wall-wart power
Many systems use 1 diode for each source of power to power the system from whichever input voltage is higher, which automatically handles the "smoothly transitions" requirement.
The diode works fine on the wall-wart power side.
USB power
Alas, a diode on the USB-power side wouldn't work for the Arduino.
When running off USB power alone, a diode drop (typically about 0.6 V) would cause everything to run a diode drop lower than USB power -- so it would have been typically 4.4 V, which is apparently (?) inadequate.
mystery parts
Later versions of the Arduino schematic clearly label the 3-pin box "powersupply DC 21mm", indicating a 21 mm barrel plug.
The mysterious "4" and "8" pins in the top-left of the Arduino schematic are the power pins of an 8-pin dual op-amp.
That op-amp is used here as a comparator.
thoughts
I don't know why the designer didn't use a comparator IC, or why the designer used both op-amps in the package when just one op-amp is adequate -- but since it clearly works, I'm not going to say it is "wrong".
The op-amp and the pFET implement something very close to an "ideal diode": when only the USB cord is plugged in, the op-amp drives the pFET hard ON, giving a voltage drop across the pFET less than 0.1 V (so everything runs on something close enough to 5.0 V).
When a person plugs in a USB cord to an Arduino that previously had nothing plugged in, the body diode of the pFET "T1" lets power from the USB cable leak in enough to bootstrap the op-amp power supply voltage up to about 4.6 V, more than enough to power up the op-amp, which then turns that pFET hard ON, pulling the voltage the rest of the way up to more than 4.9 V.
When a person plugs the wall-wart into the Arduino power jack, the op-amps turn the pFET hard OFF.
The pFET body diode prevents power from the voltage regulator back-washing to the USB host.
In principle USB power could continue flowing through the pFET body diode into the Arduino, but that's going to be pretty insignificant since the USB power is close to the same voltage as the regulated voltage generated from the wall wart.
p.s.:
When a tiny company sells 250 000 boards, I personally use the word "successful" rather than "dummies".