**Core Concept**
The posterior superior alveolar artery is a branch of the maxillary artery, which is a terminal branch of the external carotid artery. This artery supplies the posterior teeth of the maxilla, including the molars and premolars.

**Why the Correct Answer is Right**
The maxillary artery is responsible for supplying blood to the face, including the upper teeth and palate. The posterior superior alveolar artery is one of its terminal branches, which specifically supplies the posterior teeth of the maxilla. This artery plays a crucial role in maintaining the health and function of the teeth and surrounding tissues.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the posterior superior alveolar artery is not a branch of the internal carotid artery, which primarily supplies the brain and the eyes.
* **Option B:** This option is incorrect because the posterior superior alveolar artery is not a branch of the external carotid artery's other terminal branch, the superficial temporal artery, which supplies the scalp and face.
* **Option C:** This option is incorrect because the posterior superior alveolar artery is not a branch of the facial artery, which primarily supplies the face and lips.

**Clinical Pearl / High-Yield Fact**
The posterior superior alveolar artery is a common site for dental procedures and should be carefully identified and avoided during dental surgery to prevent bleeding and other complications.

**Correct Answer:** C.