Pretty much on the point, but technically it's all about the trade-off between stopping distance and stopping force.
Imagine you are pushing a shopping trolley around (one's head), and that shopping trolley contains a pack of eggs (one's brain).
If you drive the shopping trolley blindly, at speed, into a brick wall, the eggs keep going and smash into the front of the trolley. (Very short stopping distance, maybe like a fraction of a millimeter, so the stopping forces are VERY high )
If you drive the shopping trolley at the same speed, but see the brick wall coming, and haul back on the shopping trolley at the last minute, the eggs will still slide forward, but with less force, i.e. hopefully not enough to break them. Clearly the sooner you see the brick wall coming, the more gently you can decelerate the trolley, and therefore the less force the eggs experience when they touch the front of the trolley. Optimally you stop entirely before the actual crunch.
The foam in a helmet/halo/whatever, is providing that last minute controlled deceleration of the head and it's
eggs cargo. Which is why having sufficient foam thickness is SO critical, because it's all about starting the controlled deceleration early enough, i.e. before the brick wall (of head to ice) hits, so the forces are low enough to be survivable.
Anyone for omelettes for breakfast?