**Core Concept**
Battle's sign refers to the clinical manifestation of a specific type of head injury, specifically a posterior cranial fossa fracture. This occurs when there is bleeding from the temporal bone's mastoid process, leading to ecchymosis (bruising) in the posterior aspect of the mastoid area.

**Why the Correct Answer is Right**
Battle's sign is indicative of a basilar skull fracture, which is often associated with temporal bone fractures. The temporal bone's mastoid process is a common site of fracture in such cases, leading to bleeding and subsequent ecchymosis. This sign is clinically significant as it suggests a possible fracture of the posterior cranial fossa, which may have implications for the patient's management and prognosis.

**Why Each Wrong Option is Incorrect**
**Option A:** Hemorrhage around the eyes is known as periorbital ecchymosis or "raccoon eyes," which is a different sign of head injury, often associated with anterior basal skull fractures.
**Option C:** Umbilical ecchymosis is not a recognized sign of head injury and is more commonly associated with abdominal trauma.
**Option D:** Vaginal ecchymosis is not a relevant sign in this context and is not associated with head injuries.

**Clinical Pearl / High-Yield Fact**
In the context of head injury, it is essential to remember that Battle's sign, along with other signs such as periorbital ecchymosis and cerebrospinal fluid (CSF) rhinorrhea or otorrhea, can indicate a possible basal skull fracture. These signs should prompt further investigation and management to prevent potential complications.

**✓ Correct Answer: B. Mastoid ecchymosis**