The question tests which named structure traverses the foramen magnum. Think of the foramen magnum as the gateway where the brainstem becomes the spinal cord. Walking through it you would find the medulla oblongata wrapped in meninges, the two vertebral arteries climbing into the cranium, the single anterior and paired posterior spinal arteries, the spinal portion of the accessory nerve, and supporting ligaments such as the apical ligament of the dens and the tectorial membrane.
From the four options, only the vertebral artery clearly belongs to this list. It ascends through the transverse foramina of the upper cervical vertebrae, then pierces the dura and arachnoid and enters the skull through the foramen magnum to join its fellow and form the basilar artery.
The internal carotid artery uses a completely different route, the carotid canal in the petrous temporal bone, so it is excluded. The sympathetic chain stays outside the skull entirely, lying along the vertebral bodies in the neck and thorax. The accessory nerve is a deliberate trap: only its spinal root passes upward through the foramen magnum, while the nerve trunk leaves the skull through the jugular foramen, so labelling cranial nerve XI as the foramen magnum structure is incorrect.
$\therefore$ the vertebral artery is the structure that passes through the foramen magnum.
\[\boxed{\text{Vertebral artery}}\]