Load a beam and it bends, and the material inside it does not all work the same way. This diagram cuts the beam at mid-span so you can see one face stretching and the other squeezing, with the stress fading to nothing along the middle.
A beam is a bar that carries load across a gap. When a load pushes it down, the beam does not simply squash — it bends, curving so that one side of the bar is stretched and the other is squeezed. That is where stress comes from: the material resisting being pulled apart on one face and pushed together on the other.
The diagram shows a beam resting on two supports with a load at the middle. It sags slightly, and a cut marked A–A at mid-span is drawn enlarged on the right, revealing what is happening inside the material.
The coloured band across the section shows how hard the material is working. It is strongest (orange) at the compressed top face and at the stretched bottom face, and it fades to nothing (blue to pale) along the neutral axis running through the middle. On one side of that line the material pulls, on the other it pushes.
A downward load at mid-span pushes the beam out of a straight line. The bar curves, and because it is rigid enough not to break, it resists by stretching on one face and squeezing on the other.
On top of the curve the material is pushed together — compression. Underneath it is pulled apart — tension. Both are stresses, just in opposite directions.
The further a point sits from the middle of the section, the harder it is stretched or squeezed. So the top and bottom surfaces carry the highest stress, which is exactly why an I-beam puts its metal out at those faces.
Right through the middle of the section runs the neutral axis. Material there is neither stretched nor compressed, so its stress is zero — it barely helps carry the bending.
Cutting the beam at mid-span and looking at the face reveals the whole picture at once: compression above, tension below, neutral axis in the middle, and stress growing steadily outward from that line.
When a load bends a beam, the material on the outside of the bend is stretched and the material on the inside is squeezed. Those stretching and squeezing forces are the stress, and they grow the further a point lies from the middle of the section.
The neutral axis is the line across the beam section where the material is neither stretched nor compressed, so the stress is zero. On one side of it the material is in tension and on the other in compression.
At the top and bottom surfaces, furthest from the neutral axis. That is why a beam is shaped like an I: most of the material is placed near those surfaces where it does the most good.
Because the stress there is zero. Material squeezed into the middle of a section resists very little bending, so engineers move it toward the surfaces instead.
A lot. The stress at a surface depends on its distance from the neutral axis, so widening the flanges of a section or moving material away from the middle raises its bending strength without adding weight.