Drought is caused by a weather pattern which consistently results in descending air over a region. The Atacama Desert is an example of a region where this condition of descending air is, with very rare exceptions, permanent. If air is constantly descending, even if a region is hot and near the sea, it is nearly impossible for rain to fall as descending air grows denser and hotter as it descends, becoming more able to hold water vapor.
Descending air in regions near the equator such as the Atacama Desert is associated with the Intertropical Convergence Zone, a humid, rainy area near the equator where air is constantly rising. That air as it rises, cools and the water vapor in it is precipitated. The air then goes to the north and south and falls, returning to the surface in a circular rotation associated with the trade winds.
Generally the Intertropical Convergence Zone moves north and south with the seasons, moving north when it is summer in the northern hemisphere and south when it is summer in the southern hemisphere, it is the movement of this zone which results in the dry and wet seasons associated with subtropical climates. In the region of South American this north-south movement is slight resulting in the stable dry spot of the Atacama Desert.
Unusual movements of Intertropical Convergence Zone may result in unexpectedly dry seasons, or droughts, for example in Australia, California and the Mediterranean. It is sometimes theorized that global warming will increase the frequency and intensity of such incidents due to increased energy being added to the weather pattern associated with the Intertropical Convergence Zone. Thus droughts might be expected further north (or south) than they usually occur. This has been advanced as a possible reason for recent droughts in Spain and Turkey.
Descending air is associated with a high pressure area or anticyclone. This can be visualized a "hill" of dry air. Air is constantly rolling off of the top of the hill and descending as dry wind. There are certain regions such as the dust bowl region of the Southern Plains in the United States, where this kind of air mass can form and remain stable. Think of it as centered on the Oklahoma Panhandle. When this high sets up, and is not disturbed by air masses arriving from the Pacific or the Gulf of Mexico, it will not rain until something disturbs it. Generally some front will arrive from the west which will push the hot dry air out, but if the fronts move to the north, say across the Dakotas, the air mass will just sit there. There are other areas in the interior of continents where this condition can develop, for example, in the interior of Central Asia. When it occurs, as it did recently, in a usually well watered region such as the southeastern United States in Georgia and Florida, it is a notable crisis, as the infrastructure and economics of the region are set up for normal rainfall.