What is Traction and the stress tensor?

Cut the solid, in thought, along a small surface $\dd S$ of normal $\vect n$: the material on the $+\vect n$ side pulls on the other side with a force $\dd\vect F = \boldsymbol\sigma(\vect n)\,\dd S$ — the traction. This force depends linearly on $\vect n$ (Cauchy), so it is encoded by the stress tensor $\sigma_{ij}$:

in pascals. $\sigma_{xx}$ is a pull ($> 0$: tension) or push ($< 0$: compression) across a face normal to $x$; $\sigma_{xy}$ is a force along $x$ carried by a face normal to $y$ — a shear stress. A fluid at rest is the special case $\sigma_{ij} = -p\,\delta_{ij}$: pressure pushes equally on every face and shears on none, which is why fluids flow — they cannot carry static shear.