I feel like a car's transmission or a bike derailleur may be a good analogy to explain it to people, though an MPPT tracker is a ratcheting CVT.
So a 60W Solar Panel might be 12V 5-Amps in the best case scenario (directly pointed at the sun during clear skies). If you draw 5.1-Amps, suddenly the voltage drops all the way to 0.7V or some other nearly useless level.
What is annoying about solar panels is that this point changes depending on temperature, shadows, and other conditions. As the sun sets and hits the solar panel at a shallower angle with dimmer afternoon light, it might drop to 12V 2-Amps, and of course at night it will drop to 12V 0.01Amps or less.
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A MPPT circuit "tracks" this point where you can obtain the maximum amps at the maximum voltage (or really: the maximum volts * amps), and changes the current draw of the effective circuit to "find" this point.
It requires some kind of power-sink (ie: hooking it up to the wall power and assuming wall-power can take infinite amounts of energy). Or more likely, a lead-acid battery or LiFePo4 charging circuit that can "store the extra energy dump".
What I meant was that I wasn't confident that I was remembering the open-circuit voltage of a silicon solar cell, and in fact I had it wrong—it's not 0.7 volts, but 0.5 to 0.6 volts. And I couldn't remember if the diode junction was forward-biased or reverse-biased in normal operation. It's reverse-biased—the photocurrent goes the opposite direction from normal diode current. Now that I think about it, maybe that's why shade on one cell knocks out a whole string.
One quibble, though: if you maintain 12 volts in the usual direction across a series of 10 monocrystalline silicon solar cells at night you are just going to lose a subthreshold leakage current through them, because you're forward-biasing the pn junctions in the cells, just not quite by enough to turn them on. They'll emit a little bit of infrared light, a feature used to analyze solar panel failures (so-called "EL testing"). Illuminance at night is at best a million times dimmer than sunlight https://en.wikipedia.org/wiki/Orders_of_magnitude_(illuminan... and that subthreshold dark current is not going to be a million times lower than your normal current. Even under indoor lighting, which is only about 2000 times dimmer than direct sunlight, monocrystalline silicon PV cells will consume power rather than producing it.
Because of the intermittency you're describing, I suspect that thermal energy storage of various kinds (sensible heat, phase change materials, or especially TCES) is going to be important for the wide adoption of solar power, because according to my notes lead-acid batteries store about 20kJ/US$ and LFP a bit less, while industrial calcium chloride costs about US$300 per tonne (US$272/tonne according to https://derctuo.github.io/notes/desiccant-climate-control.ht...) and can absorb about its own mass of water from the air, liberating the water's enthalpy of vaporization, providing TCES.
I believe the heat thus stored is 408kJ/kg (see linked notes) which works out to 1500kJ/US$ at that price, roughly 1% of the cost of the same energy storage capacity in a battery. And, depending on the desiccant, it's plausible that you could reduce that by another order of magnitude, or two orders of magnitude for industrial installations. You can probably get by with impure calcium chloride or as-mined carnallite, for example.