Wow, what an elegant wall for a desert garden. This looks to be Organ Pipe Cactus (Lemaireocereus marinates) and a little research shows that it has often been used for natural fencing in the past. You can find more information through this Google Search on Organ Pipe Cactus.
Like hedges in the UK, I love natural barriers for those areas where you want or need to contain people, property or livestock. In most cases, living barriers require less maintenance than fences and make use of the natural plant life in a creative way.