Smack a table with your hand. What happens? It hurts because the table pushes back on your hand.
Now, smack a block of clay with your hand. What happens? It hurts less because the clay squishes and pushes back on your hand less hard.
A Styrofoam bike helmet is like the block of clay. When your head hits it the energy goes into squishing the Styrofoam rather than hurting your head.
In engineering and physics, the squishing is called a “deformation.” There’s a lot of physics around how deformations absorb forces but they are not usually covered by basic physics. Most basic physics focus on rigid body physics because it is simpler. Rigid is a thing that does not deform at all. (In real life, many materials deform, even if it’s just a little.)
A rigid helmet also distributes forces around your head so no one spot takes all the force, but others have already answered that part of the physics.
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