The reason for our desert weather and landscape is something that may seem, well, just the way it is. But, climate is always a factor of the environment around the area, from the area's nearby topography (mountains, i.e.) to it's proximity to oceans and the temperature of the ocean water to the prevailing wind direction.
Southern Arizona's Sonoran Desert is here for two reasons: 1) California mountains and 2) the cool water off the west coast.
First, let's look at prevailing wind.
The United States sits in the "mid latitudes." That means we are roughly half way between the north pole and the equator. Around the globe, areas roughly at our latitude (distance north of the equator), the prevailing wind comes out of the west. Figure 1 shows this.
Figure 1: Prevailing wind direction across the United States, when averaged throughout the year, is roughly west to east.
This west-to-east wind doesn't blow right off the ocean, through California and into Arizona. Instead, it must cross the mountains of southern California before reaching Arizona.
The air is forced uphill as it moves west-to-east. When air rises, the atmospheric pressure drops and the temperature cools. Cooler air can't hold as much moisture as warmer air. So, the moisture is forced to condense into visible cloud particles. As this process continues, the drops get so big and heavy they fall as rain. Rain, notice, on the WEST side of the mountains (see Figure 2).
Figure 2: Rain forms on the west side of California's coastal mountains.
That leaves the east side of the mountains, namely Arizona, with drier air, as shown in Figures 3 and 4.
Figure 3: Rain occurs on the west side of the coastal mountain range in California.
Figure 4: Rain on the west side of the mountains robs the air of it's moisture as it continues down the mountain range into Arizona.
The next reason that southern Arizona is a desert concerns the temperature of the water off the west coast of California. Even though the mountains rob most of the moisture from the west-to-east moving wind, there isn't an exceptional amount of moisture available due to the cool temperature of the ocean off of the southern California coast.
If you've visited San Diego's beaches, you know that the water there is very chilly.
Chilly water evaporates much more slowly than warm water. Therefore, there is less moisture in the air available for rain.
The water is chilly because of a current off the west coast, called the California Current, which brings water from the Alaskan coast south to the beaches of San Diego. Obviously, with the water originating in the Gulf of Alaska, it's cold!
Figure 5: The California Current brings colder water south along the west coast, resulting in cold water temperatures and less evaporation, which corresponds to less available moisture for rain.