Well, lime – or, rather, quicklime – is indeed produced inside a lime kiln. And it is achieved, basically, by the heating of limestone to 900-1,000°C, at which temperature the stone ‘calcinates’, or breaks down. Carbon dioxide is given off, leaving calcium oxide – or quicklime. In other words:
CaCO3 + heat = CaO + CO2
or,
Limestone + heat = quicklime + carbon dioxide
Quicklime is really useful stuff, and can be used in mortar/plaster, paper/glass/steel production, sewerage treatment, etc., but is especially handy in agriculture (to counter acidic soils) and to hide the smell of decomposition in open graves (plague outbreaks, and the like). Curiously, before electric lighting came along it was used in theatres as an illuminant – as it glows brightly when heated to high temperatures (hence ‘limelight’). Anyway, historically, at least, there was quite a demand for the stuff.
The thing is, quicklime is rather unstable. Left to its own devices it will react naturally with carbon dioxide in the atmosphere and revert to its ‘natural’ limestone state. Transportation, therefore, is/was a problem – as was easily lumping about the limestone, and, indeed, the coal needed to heat the kilns themselves. So, this is why you find so many lime kilns near the coast: easy to get the limestone/coal in, and easy to get the quicklime out. So quayside spots like those at Seahouses and Beadnell were perfect. Improvements in the transportation network during the nineteenth century led to many more inland (and often much larger) sites being developed.
So the next time your little sidekick asks the question, you know exactly what to say. And, moreover, you’ll know precisely what you’re talking about.