**Core Concept**
The superior gluteal nerve is a branch of the lumbosacral plexus, specifically originating from the dorsal divisions of L4, L5, and S1 nerve roots. It is responsible for innervating the gluteus medius, gluteus minimus, and tensor fasciae latae muscles.

**Why the Correct Answer is Right**
The superior gluteal nerve supplies the gluteus medius, gluteus minimus, and tensor fasciae latae muscles, facilitating hip abduction and external rotation. This is essential for maintaining balance and stability during activities like walking or climbing stairs. The gluteus maximus muscle, on the other hand, is primarily innervated by the inferior gluteal nerve.

**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect because gluteus medius is indeed supplied by the superior gluteal nerve.
**Option B:** Incorrect because gluteus minimus is also supplied by the superior gluteal nerve.
**Option C:** Incorrect because tensor fasciae latae is the third muscle innervated by the superior gluteal nerve.

**Clinical Pearl / High-Yield Fact**
The superior gluteal nerve is often at risk during surgical procedures involving the gluteal region, such as hip arthroplasty or gluteal muscle repair. It's essential for surgeons to identify and preserve this nerve to avoid postoperative weakness or paralysis of the hip abductors.

**Correct Answer: D.** Gluteus maximus