**Core Concept**
The atlanto-axial joint is a synovial joint that allows for rotational movement between the first (atlas) and second (axis) cervical vertebrae. This joint is crucial for the flexion, extension, and rotation of the head.

**Why the Correct Answer is Right**
The atlanto-axial joint is a pivot joint, specifically a synovial pivot joint, where the dens (odontoid process) of the axis vertebra rotates within the ring of the atlas vertebra. This unique joint enables the rotational movement of the head, which is essential for activities like looking over the shoulder. The joint is stabilized by ligaments, including the transverse ligament of the atlas, and is also supported by muscles such as the sternocleidomastoid.

**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect because the atlanto-axial joint is not a ball-and-socket joint, which typically allows for a wide range of movement in multiple directions.
**Option B:** Incorrect because the atlanto-axial joint is not a hinge joint, which only allows for flexion and extension in one plane.
**Option C:** Incorrect because the atlanto-axial joint is not a gliding joint, which allows for sliding movement between flat surfaces.

**Clinical Pearl / High-Yield Fact**
The atlanto-axial joint is susceptible to injury, particularly in cases of trauma or rheumatoid arthritis, which can lead to subluxation or dislocation of the joint. This can result in neurological deficits, including quadriplegia, if left untreated.

**Correct Answer: C. Synovial pivot joint.**