Hi,

Von Mises stress is simply some kind of equivalent stress used  to evaluate the 'total' stress. It is a combination of stresses acting in multiple (so-called principal) directions. Maximum number of these directions is 3 (for a 3-dimensiona solid). Von Mises stress is one of many stress quanitities which is used to define an overall stress value for some structure. If you consider a 1D bar loaded in uniaxial tension, the Von Mises stress will simply equal the applied stress in de laoding direction. Note that this is only true for uniaxial tension, where the bar is free to contract, resulting in zero stresses perpenicular to the laoding direction. Constraining lateral deformation of the bar will result in nonzero stresses in lateral directions, yielding the Von Mises stress to be unequal to the applied stress

As I already mention the Von Mises stress is a combination of the 3 principal stresses. Principal stresses are simply stresses which act normal to the principle planes. These planes are planes where the shear stresses equal zero. A rondomly oriented material point can be rewritten in such a way that all shear stresses are elimanted, thus resulting in only three stress components, which are the principal stresses. If you again consider a simple uniaxial bar, the following holds:

Von mises stress = principal stress = applied stress.

For more insight you should consult some articles on (3D) elasticity. There is plenty of literature available.