What exactly does it mean when blood pressure on the left is significantly higher than on the right?

Differential BP. If correctly taken, that could mean that you have a narrowing of one of the central arteries on the right. This could indicate a right subclavian artery stenosis. Nothing can increase blood pressure in one arm, but a blockage will decrease blood pressure. So the correct blood pressure is the highest value or the blood pressure in the left arm.
R Arterial disease. The right arm has arterial disease which lowers the pressure in that limb.