**Core Concept:**
Gram-negative bacteria are a type of bacteria that stain Gram-negative during the staining process. They have a thin peptidoglycan layer in their cell wall, which allows the crystal violet stain to penetrate and bind to the cell wall. This distinguishes them from Gram-positive bacteria, which have a thick peptidoglycan layer that prevents the crystal violet from penetrating and binding, resulting in a Gram-positive stain.

**Why the Correct Answer is Right:**
Gram-negative cocci refers to a specific group of Gram-negative bacteria that exhibit coccal (spherical) shape. In this case, the correct answer represents a type of bacteria with the following properties:

1. Gram-negative staining during the staining process.
2. Coccal (spherical) shape.

Gram-negative bacteria are important to recognize and differentiate due to their unique characteristics, such as their potential to cause various infections and their resistance to certain antibiotics.

**Why Each Wrong Option is Incorrect:**
Option A (Gram-positive cocci) and Option B (Gram-positive rods) are incorrect because they describe Gram-positive bacteria, which have a thick peptidoglycan layer and exhibit Gram-positive staining during the staining process.

Option C (Gram-negative bacilli) is incorrect because it refers to Gram-negative bacteria with a rod-shaped (bacilli) structure, not coccal (spherical) shape.

**Clinical Pearl:**
Recognizing the key features of Gram-negative bacteria, such as their Gram-negative staining and coccal shape, is essential for accurate diagnosis and appropriate treatment of infections caused by these bacteria. Understanding the differences between Gram-negative and Gram-positive bacteria is crucial in the field of microbiology and infectious diseases.