Principal stresses are the maximum and minimum values of the normal stress that acts on an object. Normal stresses are the stress components that act perpendicularly to an imaginary plane on the object.
An example of these stresses is a box sitting on the floor. The gravitational force pulls the box down, while the floor exerts a normal force on the box that prevents it from being in a constant state of free fall. If there were irregularities in the floor that caused one area in contact with the box to be greater and another to be smaller, these would be the principal stresses.