Normal loads applied in 3 orthogonal axes. Say you had a cube of material. If a normal load is applied to all six faces then you would have triaxial stress.
I have not heard the term triaxial tensile stress before. Triaxial stress is the most general state of stress and would mean stress in all three directions. Stress is a symmetric tensor. Therefore it requires six components to completely define the state of stress at a point; Three normal stresses and three shear stresses. Tensile stress is a normal stress that tends to stretch the length of a part.
