**Core Concept**
Hyperparathyroidism is a disorder of calcium and phosphate metabolism caused by an overproduction of parathyroid hormone (PTH), leading to increased bone resorption, renal calcium wasting, and hypercalcemia.

**Why the Correct Answer is Right**
The most common cause of primary hyperparathyroidism is a solitary parathyroid adenoma, which accounts for approximately 85% of cases. This adenoma results in an autonomous secretion of PTH, independent of calcium levels, leading to the characteristic clinical and biochemical features of hyperparathyroidism. The remaining 15% of cases are typically due to parathyroid hyperplasia, a condition where all four parathyroid glands are enlarged.

**Why Each Wrong Option is Incorrect**
* **Option A:** While secondary hyperparathyroidism can occur in conditions such as chronic kidney disease, it is not the most common cause of hyperparathyroidism.
* **Option B:** Familial hypocalciuric hypercalcemia is a rare genetic disorder that can cause hypercalcemia, but it is not the most common cause of hyperparathyroidism.
* **Option D:** While parathyroid carcinoma is a rare cause of hyperparathyroidism, it is not the most common cause.

**Clinical Pearl / High-Yield Fact**
Parathyroid adenomas are often located in the inferior parathyroid glands, which are more commonly involved in primary hyperparathyroidism.

**Correct Answer: C.**