**Core Concept**
Hemophilia is a genetic disorder characterized by a deficiency or dysfunction of certain clotting factors in the blood, leading to impaired blood coagulation. This results in an increased risk of bleeding, particularly into joints and muscles.

**Why the Correct Answer is Right**
The most common manifestation of hemophilia is joint bleeding, known as hemarthrosis. This occurs due to the accumulation of blood in the joint space, which can cause pain, swelling, and long-term damage to the joint. The repeated episodes of joint bleeding can lead to chronic joint disease, including osteoarthritis and joint deformity. The bleeding into joints is particularly common in hemophilia A, which is caused by a deficiency of factor VIII.

**Why Each Wrong Option is Incorrect**
* **Option A:** While hematemesis (vomiting blood) can occur in hemophilia, it is not the most common manifestation.
* **Option B:** Hematuria (blood in the urine) can occur in hemophilia, but it is not the most common manifestation.
* **Option C:** Hemorrhage (excessive bleeding) can occur in hemophilia, but it is not specific enough to be the most common manifestation.

**Clinical Pearl / High-Yield Fact**
The "bleeding into joints" in hemophilia is often a result of the accumulation of blood in the joint space due to the disruption of the joint capsule, which can be caused by minor trauma or even trivial injuries.

**Correct Answer:** C. Hemarthrosis.