**Core Concept**
The pudendal nerve is a nerve that arises from the S2-S4 nerve roots and is responsible for supplying the muscles of the perineum, including the external anal sphincter. It plays a crucial role in maintaining continence and facilitating voluntary control over the anal sphincter.

**Why the Correct Answer is Right**
The external anal sphincter is a skeletal muscle that surrounds the anal canal and is responsible for maintaining continence. The pudendal nerve, specifically its inferior rectal nerve branch, provides motor innervation to the external anal sphincter. This allows for voluntary control over the anal sphincter, enabling individuals to maintain or release feces. The pudendal nerve achieves this through the release of neurotransmitters that stimulate the contraction of the external anal sphincter muscle.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the pudendal nerve does not supply the external anal sphincter through its superior rectal nerve branch, which is primarily responsible for parasympathetic innervation of the rectum and the internal anal sphincter.

**Option B:** This option is incorrect because the inferior rectal artery, not the pudendal nerve, supplies the external anal sphincter with blood.

**Option C:** This option is incorrect because the obturator nerve, not the pudendal nerve, supplies the adductor muscles of the thigh.

**Clinical Pearl / High-Yield Fact**
The pudendal nerve is also responsible for supplying the muscles of the perineum, including the bulbospongiosus and ischiocavernosus muscles, which are involved in the maintenance of the pelvic floor and the regulation of sexual function.

**Correct Answer:** C.