Can you explain how a carotid surgery to remove plaque works?

Like an onion. Arteries have layers similar to onions, but only 3. The disease which causes the blockage (atherosclerosis / plaque formation / cholesterol build-up) involves the inner 2 layers. During surgery we expose the carotid artery, clamp above and below the blockage, open the artery up and literally separate the inner 2 diseased layers from the outer strength layer, just like layers of an onion.
Plaque removal. The inner two layers of the artery are essentially pealed out. The plaque is actually removed down to a clean plane. This removes the obstruction to the blood flow and the debris that may cause a stroke.