Sadly you're no further forward with Googles "explanation" Charles! It only tells you what you already knew!
Think of the alternator as a battery charger, powered by the engine turning. A bit like an overgrown dynamo which in some ways it is but a dynamo puts out dc current (the same as a battery) but is nowhere near as efficient as an alternator.
The alternator on the other hand puts out ac (alternating) current so needs to be rectified which is done inside the alternator to give a dc output. Because it is much more efficient than a dynamo, it gives a higher output at idle than a dynamo.
Both need some sort of voltage regulator to prevent overcharging (and undercharging) which until relatively recently, were set to 14.4V cold, 14.0V hot. Alternators generally have the voltage regulator built in for many reasons but to know why those figures are arrived at, you need to know a little about the battery itself.
The humble 12V battery is in fact a 13.2V battery, made up of 6 x 2.2V cells. Each cell needs a minimum of 0.1V more than its voltage to charge, hence the 13.8V minimum voltage needed to charge a battery.
When a car has just been started, the regulator will be cold and the battery will need more charge put in to recover more quickly. That's why a cold regulator gives 14.4V output, 0.2V per cell more than normal. This allows the alternator to put more current into the battery because the battery has a certain internal resistance.
From Ohms Law, resistance x current = voltage and that formula can be transposed whichever way you like. For example, a 12V bulb that takes 10A will have a resistance of 1.2 Ohms. You can rework this example so if a battery is being charged at 14.4V @ 40A, the resistance will be 0.36 Ohms. Because the voltage regulator senses the battery voltage either with a thin wire from the battery +ve terminal (battery sensed) or from taking a feed from the alternator output terminal (machine sensed), it can monitor the voltage and regulate the rotor current in the alternator.
The rotor generates a magnetic field which spins inside the stator (the stator is the middle part of the alternator, often "red-lead" colour or sometimes black and has the windings that produce the output current) and depending how much power is fed into the rotor, alters the output of the stator.
If the battery is up to voltage, very little power is fed into the rotor so the alternator doesn't put very much out in the way of current. If the battery voltage is low, it feeds more power into the rotor which in turn generates more power in the stator.
As you can see, the voltage regulator monitors the battery voltage and alters the alternator output to suit. Assuming that the belt is tight, it can generate 14V x 70A = 980W of power which is about 1 1/3 horsepower. That means if the belt is going to slip because it's loose, it will do it when it's cold and most load is on the alternator but it can compromise the output of the alternator too.
Something to bear in mind is that with the normal lead-acid battery, the plates inside are covered in lead-antimony to help prevent sulphation and self-discharge.
In a calcium battery, the plates are covered in silver-calcium for the same reason, it's still a lead-acid battery though so the principles hold true with minor adjustments.
The silver-calcium increases the voltage at which it starts charging by an extra 0.1V approximately so a calcium battery needs 14.7V just to start charging. The rest is similar to the normal lead-acid battery but about 0.6-0.7V higher for charging purposes.
That's why i was asking earlier if your battery was a calcium one. If it's fully charged to start with and the car is in fairly regular use, it will start off ok but over a period of time, the overall state of charge will drop. Charging overnight with an external charger usually revives it and it will function normally again for a while, at least until the overall state of charge drops again.
Note that both types of battery share the common voltage versus state of charge :
Couple of charts there for you, you'll see in the second one that it mentions SG (Specific Gravity) which can be checked with a hydrometer. You know the "Magic Eye" on some batteries? Green when it's charged, yellow when it's flat but capable of being jump started and then usually black after that? It's a simple hydrometer inside the battery.
Hopefully that gives you a bit more of an insight than Goggle did, feel free to ask if there's something i've missed or you don't get.