Relationship to stroke pathogenesis
When a carotid artery is narrowed by atherosclerotic plaque so that its cross-sectional area is reduced by 70% or more, the patient has a significantly increased risk of stroke. Narrowing of the carotid can be symptomatic, producing a stroke or transient ischemic attack (TIA), or asymptomatic. This depends on factors like whether the plaque surface is disrupted, increasing the likelihood of thrombus formation (a source of emboli) or whether there is an effective collateral circulation that supplements the blood supply to brain regions in the jurisdiction of the partially occluded carotid.

A little about control/treatment
When a carotid artery is narrowed 70% or more, carotid endarterectomy (surgical removal of obstructing plaque) is often recommended.  This procedure has been shown to significantly reduce stroke risk for both symptomatic and asymptomatic patients. Less severe blockages (30% or less) are often treated using lipid-lowering agents (statins) and antiplatelet therapy with the combined goals of slowing atherosclerotic disease and reducing the risk of thrombus formation.