I've seen that "2.1" figure so many times. How is it calculated? (Or is it just a concise and informal way of saying "a bit more than two"?)

It can be calculated, based on statistics of how many people die before reaching fertility.

But given that the statistics have wide error bars, and there are so many other intervening factors, "a bit more than two" is just as good a way to calculate it.

Well, generally it is "how many people do you need to replace the 2 people that created those people". So the baseline is 2 since you need 2 parents and to replace them you'd need 2 children in an ideal world but since not every child survives long enought to themselves be part of this cycle the .1 comes in.

I've thought about it a bit in the meantime .... In the UK only about 30 children per 100,000 die before age 18 so that would be much less significant than the fact that only about 49% of children are female. Taken together, those facts would imply that you need about 2.0414 children per woman, so 2.05 would be more than enough. So how do we get to 2.1? Perhaps the 2.1 is for other countries with higher infant mortality?

You get 2.1 because they only want to show 2 significant digits, but it's important to show that the number is greater than 2.0.

From individual families' perspectives, you can only have a whole number of kids anyway, so 2.1 vs. 2.04 isn't a meaningful difference.

Being dead isn't the only reason someone can't have kids.