Consider a stress element in a general state of stress.
The stress tensor for this element can be written as:

There are three mutually perpendicular “principal” planes where the shear stresses are zero. When viewed in this orientation, the state of stress an be written as:

The normal stresses acting on the principal planes are called principal stresses, and their directions are called principal directions.
Maximum principal stress represents maximum normal stress.
Minimum principal stress represents minimum normal stress.
This page is part of The Encyclopedia of Stresses in Solids