**Core Concept**
The prostatic artery is a vital blood vessel supplying the prostate gland, playing a crucial role in maintaining its function and health. The prostatic artery arises from the superior or inferior vesical arteries, which are branches of the internal iliac artery.

**Why the Correct Answer is Right**
The prostatic artery is responsible for supplying blood to the prostate gland, which is essential for its growth, development, and maintenance. The internal iliac artery, also known as the hypogastric artery, is a major branch of the common iliac artery that supplies blood to the pelvic organs, including the prostate gland. The prostatic artery typically arises from the superior or inferior vesical arteries, which are direct branches of the internal iliac artery. This ensures a constant blood supply to the prostate gland, facilitating its normal functioning.

**Why Each Wrong Option is Incorrect**
**Option A:** The common iliac artery is a major branch of the abdominal aorta, but it does not directly give off the prostatic artery. The common iliac artery divides into the internal and external iliac arteries, and the prostatic artery arises from the internal iliac artery, not the common iliac artery.

**Option B:** The external iliac artery is a branch of the common iliac artery, which supplies blood to the lower limb. It does not give off the prostatic artery, which arises from the internal iliac artery.

**Option C:** The internal carotid artery is a major branch of the common carotid artery, supplying blood to the head and neck region. It does not give off the prostatic artery, which arises from the internal iliac artery.

**Clinical Pearl / High-Yield Fact**
The prostatic artery is a critical blood vessel in the pelvic region, and knowledge of its origin is essential for urologists and surgeons performing prostate surgery. **Correct Answer: D. Internal iliac artery.**