Complex sentence: Mathematically, the thermal wind relation defines a vertical wind shear--a difference in wind speed or direction with height--as a function of a horizontal temperature gradient, which is a change in temperature with horizontal distance.
Split into simpler sentences: Mathematically, the thermal wind relation defines a vertical wind shear--a variation in wind speed or direction with height. The wind shear in this case is a function of a horizontal temperature gradient, which is a variation in temperature over some horizontal distance.