The canadian chap has explained a lot of things well.

The biggest part is, water vapor in the air condenses to liquid water when it encounters a surface that is colder. For example, nice warm inside bricks connected to cool outside bricks after someone put something in the cavity.

If that water condenses in a place that is cold, and low airflow, it will be there for a while. It soaks into anything that might take it, and gives a fantastic place for mould to grow.
So if the cavity filling between two walls is not executed with a serious survey and planning, this can happen.

The two main options to prevent water are putting up membranes that prevent water vapor reaching the bad area in the first place, or by using materials that are breathable to the vapor throughout the wall, so it can wick away in either direction.

So in the bad situations, you end up with water condensing, then getting trapped by non-breathable insulation, in some cases pooling up at the bottom of the cavity, leading to the damp growing effectively out of the walls, and into the room.
And of course, non-breathable materials are often cheaper/more insulating, so generally get picked first.