It is about absorbing the energy of the collision (into shattering the plastic bodywork and deforming aluminium frames at front and rear), while holding the passengers so they do not strike any surfaces, and preventing any hard or sharp things intruding into the passenger compartment.
Did you see the episode of Richard Hammond's Wonders of Nature where he through a light bulb from the edge of space down onto a rocky mountain? The bulb was held tight in a rigid tube, surrounded by soft beads, inside another rigid tube. The outer cracked, the inner shifted, but the contents were intact when they found them, days later...
That is how cars are designed. Stiff outer, soft layers, hard and tight inners.
The factor they are all trying to manage is the 'deceleration', by spreading the impact over a few more milliseconds, the forces on the occupants are reduced massively. You can have a bit of fun plugging numbers into this model: Car Crash Example
Then their is the lightness issue: if you are in a lighter car, you have less energy to deal with (if you hit a solid object), or are more likely to rebound (if struck). That helps spread the energy dissipation over time as well.
Which leaves us with the immense strength of carbon fibre shells.
The simple comparison between carbon fiber, steel and aluminum can be understood using common forms of the high-strength versions of these materials.
Compare the mechanical properties, the modulus of elasticity (stiffness) and the tensile strength (strength under tension) of these three materials:
1. Carbon fiber T700S from Toray, a standard modulus high-strength fiber, in an epoxy 250 F-cure composite
2. Alloy steel AISI 5130, a low hardenability alloy steel with moderate strength and good toughness
3. Aluminum alloy 7075-T6, a standard aerospace aluminum alloy
Modulus of Elasticity Tensile Strength Density
MPa MPa g/cm^3
CF 120 2500 1.5
Steel 205 1275 7.9
Alu 71 570 2.8
So, CF, even at its current development stage, hugely outperforms aluminium and steel and is lighter, but is possibly *too* stiff for some designed to collapse structures.