**Core Concept**
The gastric phase of gastric secretion is a physiological process involving the release of gastric acid and enzymes in response to food intake, particularly proteins. This phase is characterized by the activation of parietal cells in the stomach lining, which produce hydrochloric acid and intrinsic factor.

**Why the Correct Answer is Right**
During the gastric phase, the vagus nerve stimulates the release of gastrin, a hormone produced by G cells in the stomach antrum. Gastrin binds to receptors on parietal cells, triggering an increase in cyclic AMP (cAMP) and subsequent activation of the H+/K+ ATPase pump, leading to the secretion of hydrochloric acid. This process is crucial for protein digestion and the activation of pepsinogen to pepsin.

**Why Each Wrong Option is Incorrect**
**Option A:** This is incorrect because the cephalic phase of gastric secretion, which occurs before food enters the stomach, involves the release of gastrin and other hormones in response to the sight, smell, and thought of food.
**Option B:** This is incorrect because the intestinal phase of gastric secretion, which occurs after food enters the small intestine, involves the release of secretin, which inhibits gastric acid secretion.
**Option C:** This is incorrect because the hormonal phase of gastric secretion, which occurs in response to distension of the stomach, involves the release of gastrin and other hormones, but is not the primary mechanism of the gastric phase.

**Clinical Pearl / High-Yield Fact**
The gastric phase of gastric secretion is often referred to as the "gastric phase" because it occurs in response to food entering the stomach, but it's actually a complex process involving multiple physiological mechanisms.

**Correct Answer: A. Gastrin**