Now, there are all kinds of solutions and they all have caveats. As someone said here, old houses are build so that walls are semi-permeble, meaning that heat constantly wanders to the outside. That also means that the dew point is pretty far towards the outside in winter - water can get out of the house. If you insulate the inner wall, the dew point will move more towards the inside, meaning your walls will get wet and water will take longer to move outside. If you insulate the outside, water cannot get out at all - you must find another solution to get the moisture out of the house. It gets more complicated the more you dive into this topic.
Warm/er air can hold more moisture than cold/cooler air. If part of the house is warm, and you happen to cook and/or shower in it, it will have a high moisture content.
But water vapour diffuses through-out an enclosure. So that water in a gaseous phase will equally spread everywhere (eventually).
When it reaches the uninsulated part/s of the structure, the air is colder and so can't hold as much moisture leading to condensation. Get lots of condensation, and you have an environment that is suitable for mold growth (which can then release spores in the air and mess up indoor air quality (IQA)). Not to mention that water is a universal solvent, and so will turn your structure (stone, masonry, concrete, wood) to mush over time.
The place of condensation will most likely be a surface that is a large temperature change: so in the winter your inside is warm, and your uninsulated outside walls are cold.
Today, it's generally solved by having an airtight sheet (plastic) between the insulation and the inner wall. Sometimes placed inside the insulation. This ensures a temperature gradient that will not cause condensation inside the house.
You'll generally put a sheet that's porous but not airtight outside the insulation, to reduce heat loss due to convection and also provide an extra layer of defense against moisture damage due to wind-blown rain.
This technique necessitates good ventilation (often powered) if it's used throughout the entire house. This is to avoid saturating the inside air with humidity due to breathing and other activity, itself leading to the condensation you're trying to avoid. It can sometimes be just on e.g. floors and ceilings. Then, the rest of the structure might still be leaky enough that mostly passive ventilation will do the trick.
Older houses handle the problem by just being so leaky that condensation won't be a problem.
