**Core Concept**
Darier's sign is a clinical manifestation characterized by the appearance of urticaria or whealing at the site of a skin lesion upon gentle stroking or scratching. This phenomenon is typically seen in conditions where there is an abnormal accumulation of histamine in the skin, leading to mast cell degranulation and subsequent release of histamine.

**Why the Correct Answer is Right**
Urticaria pigmentosa is a rare skin disorder characterized by an abnormal accumulation of mast cells in the skin, leading to an increased sensitivity to mechanical stimuli. When the skin affected by urticaria pigmentosa is stroked or scratched, the mast cells degranulate, releasing histamine, which in turn causes the characteristic whealing or urticaria. This is known as Darier's sign and is a diagnostic hallmark of urticaria pigmentosa. The histamine release is mediated through the action of tryptase, an enzyme released from mast cells, which cleaves histamine from its precursor molecule, histidine decarboxylase.

**Why Each Wrong Option is Incorrect**
**Option A:** Darier's disease, also known as keratosis follicularis, is a rare genetic disorder affecting the skin, but it is not associated with Darier's sign.
**Option C:** Allergic vasculitis is a type of inflammation of the blood vessels, but it is not typically associated with Darier's sign.
**Option D:** Atopic dermatitis, also known as eczema, is a chronic inflammatory skin condition, but it does not typically exhibit Darier's sign.

**Clinical Pearl / High-Yield Fact**
Remember that Darier's sign is a diagnostic clue for conditions characterized by an abnormal accumulation of mast cells in the skin, such as urticaria pigmentosa. This sign is not pathognomonic but is highly suggestive of urticaria pigmentosa.

**✓ Correct Answer: B. Urticaria pigmentosa**