Take a look at the anatomy of the upper cervical spine. Three muscles attach to the skull, atlas (C1) and axis (C2). Through this triangle of muscles, known as the suboccipital triangle, passes the C1 nerve, vertebral artery, and venous plexus.
The muscles of the suboccipital triangle are responsible for fine movement of your head. The big muscles like the trapezius, sternocleidomastoid and other large muscles move the head but there motion is refined by the smaller muscles of the suboccipital triangle.
You can see that 2 of the 3 muscles attach to the transverse process of the atlas. If the atlas is out of alignment, the movement of these muscles will be affected along with the nerve and blood supply to the head.
When the misalignment is corrected through an adjustment, the rapid influx of blood and nerve impulses can cause the feeling of lightheadedness or dizziness.