By spreading and absorbing the force of impact.
Your head is kinda rounded, meaning that if you hit even a flat surface, the contact area between head and surface is fairly small.
Meaning all the force of the impact has to go through a small area and quickly gets quite high.
With a helmet, whose inside is more like the shape of your skull, the force of impact is spread over a larger area, meaning the spread-out force becomes lower.
Less force, less damage.
Also, while a helmet feels firm to the touch, if you bang it hard, it'll compress.
And compressing the helmet material soaks up energy that otherwise would have gone into your skull. Less energy, less damage.
The last thing a helmet will do is to break apart. And just like it takes energy to break a stick, breaking a helmet ALSO takes energy.
And the energy that gets used up breaking a helmet, is ALSO energy that's been prevented from going into your head, doing damage there.
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Yes. I cracked mine when I fell, it could have been my head! So have one on all the time, it could save your life!!!