It's a fancy term for a particular kind of random.
And it's a model. The model is based on a large population, each member of which has an equal chance of running into any other member of the population under the same conditions. Think about your city or town--when you're going through your day, is every encounter with another person chance, equally likely to be anybody else in the city, and under the same circumstances?
No. We form networks. I interact with some people fairly often. Others I don't interact with at all. My interactions are not random, nor equal in context and circumstance. We live in networks that interconnect. In NYC, the networks interconnect a lot on sidewalks, crowded stores, and mass transit. Even in Texas, the spread happened first along the two north-south connectors from south to Dallas. I-35 and I-45, 45 being the stronger link.
So it's possible that this bug circulated in some networks before being noticed first in Wuhan.
With very small numbers there might not be an explosion. We see progressions like 1 - 2 - 4 - 8 - 16 - 32 bandied about, but that's facile. What if that first person "1" doesn't run into two people that he infects? What if the second person he infects doesn't infect anybody?
Then it goes 1 - 1 - 1 - 1 - for a while. Strikes me that this is very possible in narrow networks. You interact with 2-4 people per day, and it's pretty much the same people each day, you'll nail one with the virus over the course of a week. That person has the same kind of network, being the link between the one you're in and other one, and it spreads the same way. Low rates of transmission. And most of that in families. Which is what the earliest reports said.
Now, rethink that first progression. Yeah, it's
1 - 2 - 4 - 8 - 16 - 32
But really it's just as much
1 - 1 - 2 - 4 - 8 - 16 - 32
... -1 - 2 - 4 - 8 - 16 - 32
Think of each branch as starting a new "first person". Any branch (or network) can die out. Any branch can do the 1 - 1 - 1 - 1 thing for a while.
Stochastic. Back in March a lot of states had positive test results like 3 - 6 - 4 - 3 - 4 - 6 - 8 - 5 - 6 - 3 - with no real trend. A lot of random chains with a lot of 1 - 1 - 1 - 1 transmissions. The "superspreader" finding fits in well with this. Most chains don't branch much, and many of them die out--but in some cases instead of 1 - 1 - 1 it goes 1 - 10 - 11 - 10 - 11 - 22 - as 1 spreads it to 10, then another 1 spreads it to 10. Of course, the wider it's spread, the more likely superspreaders will abound.
And early on, that superspreader may only spread it to his narrow network of 3-4 people.
Now flip the question. Don't look for "what prevented it from exploding in December?" (in Wuhan) look instead for "what caused it to explode in December in Wuhan?" This virus was around for a while. "Not exploding" is the default.
Perhaps the RNA mutated. Perhaps it just randomly hit a superspreader that chained to another superspreader? Conditions matter--damp and cold facilitate it. Crowded conditions help. Loud speaking--forceful articulation with high air flow--helps. A librarian is not likely to be a superspreader. Somebody shouting for attention in a crowded seafood market is more likely.
Suddenly it's not a person linking one network to another, but a nexus where 50 or 100 networks cross.
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