When a strong high pressure sets up over the Great Basin, the winds that result are warm and dry from passing over the deserts to the east of the Sierra Nevada mountains. As the wind goes through passes and valleys of Santa Ana, it is made stronger through an effect similar to wind between tall buildings in a city.
This high pressure air than seeks to fill the low pressure void on the coast and pushes back over the many mountain ranges that cover Southern California toward the Pacific. As this higher pressure air comes over these mountains and drops down it is heated causing the very warm or hot temperatures associated with the Santa Anna's and the high winds as this hot and dry air is channeled, compressed and forced out through the canyons and passes. This produces sustained winds of 20 or so miles per hour with gusts into the 40's and even 60's with some being reported as high as 100 miles per hour near the peaks.