**Core Concept**
Brown-Séquard syndrome is a clinical condition characterized by hemisection of the spinal cord, resulting in ipsilateral weakness or paralysis, loss of proprioception, and contralateral loss of temperature and pain sensation. This condition arises due to traumatic injury or surgical damage to one side of the spinal cord.

**Why the Correct Answer is Right**
Brown-Séquard syndrome typically involves the following components:
- Ipsilateral weakness or paralysis due to damage to the corticospinal tract
- Ipsilateral loss of proprioception due to damage to the posterior columns
- Contralateral loss of temperature and pain sensation due to damage to the spinothalamic tract

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because loss of vibration and position sense (proprioception) is a component of Brown-Séquard syndrome, typically on the same side as the lesion.

**Option B:** This option is incorrect because loss of temperature and pain sensation is a component of Brown-Séquard syndrome, typically on the opposite side of the lesion.

**Option C:** This option is incorrect because weakness or paralysis is a component of Brown-Séquard syndrome, typically on the same side as the lesion.

**Clinical Pearl / High-Yield Fact**
The key to diagnosing Brown-Séquard syndrome lies in the dissociated sensory loss, where pain and temperature sensation are lost on the opposite side of the lesion, while proprioception and vibration sense are lost on the same side.

**Correct Answer:** D.