The maxillary artery is an extremely large artery that reaches most of the important areas of the face including the mouth, teeth, nose, muscles, and more.
The branches of this artery are located within three divisions where there are five branches to each division. The mandibular division leads down to the mandible and runs along many of the teeth. It also runs to the meninges, which is protective tissue that covers the brain and spinal cord.
The pterygoid division runs to some of the muscle groups in the face and contains the temporal arteries.
The pterygopalatine division contains all of the end branches of the arteries including the one that runs to the pharynx (the tube that connects the mouth and nasal passage with the esophagus) and the nose.