**Core Concept**
The case fatality rate (CFR) is a measure of the severity of a disease, defined as the proportion of deaths within a defined population of individuals with a particular condition over a specific time period. A high CFR indicates that the disease is more likely to be severe and fatal.

**Why the Correct Answer is Right**
A high case fatality rate suggests that the disease has a high mortality rate, meaning that a significant proportion of individuals who contract the disease will die from it. This is often due to the disease's pathophysiology, which may involve severe organ damage, overwhelming immune response, or rapid progression to a critical stage. The CFR is an important metric in determining the severity of a disease and guiding public health interventions.

**Why Each Wrong Option is Incorrect**

**Option A:** This option is incorrect because a high case fatality rate does not necessarily indicate a high incidence of the disease. Incidence refers to the number of new cases occurring within a population over a specific time period, whereas CFR is a measure of the severity of the disease.

**Option B:** This option is incorrect because a high CFR does not necessarily mean that the disease is contagious or easily transmitted. Transmission and severity are two distinct aspects of a disease, and a high CFR does not directly imply a high transmission rate.

**Option C:** This option is incorrect because a high CFR does not necessarily mean that the disease is rare. Rarity and severity are also distinct aspects of a disease, and a high CFR can occur with relatively common diseases if they are severe and fatal.

**Clinical Pearl / High-Yield Fact**
Remember, a high case fatality rate is a red flag for a disease's severity and potential public health threat, and should prompt immediate investigation and intervention.

**Correct Answer:** C.