|Control of stomach acid
Delta cells (δ-cells or D cells) are somatostatin-producing cells.
They can be found in the stomach, intestine and the Islets of Langerhans in the pancreas.
In rodents delta-cells are located in the periphery of the islets; in humans the islet architecture is generally less organized and delta-cells are frequently observed inside the islets as well.
In the electron microscope, delta-cells can be identified as cells with smaller and slightly more compact granules than beta cells.
D cells contain CCKBR (which respond to gastrin) and M3 receptors (which respond to Ach). Respectively, these receptors will increase somatostatin output and decrease somatostatin output from the D cells.
VIP, vasoactive intestinal peptide, acts positively on D cells resulting in more somatostatin being released.
Clinical significance 
A tumor of the delta cells is called a "somatostatinoma".
When a person is infected with H. pylori the lower region of the stomach, the antrum, is predominantly inflamed. This is where most of the D cells in the stomach are. The bacteria produce a cloud of ammonia around themselves using urease to protect them from the stomach acid; however, this reacts with the acid producing ammonium which is toxic to cells. This leads to many of the D cells dying and therefore a lower level of somatostatin being secreted. This results in higher levels of gastrin and stomach acid being secreted. This, combined with the damage from ammonium, leads to ulceration of the stomach wall. 
- ^ Lecture, "Function of the Stomach and Small Intestine" Deakin University School of Medicine - October 15, 2012