What is atherosclerotic calcifications of the intracranial internal carotid arteries?

When looking at a phrase like this, it is easiest to break it down into individual Words, until you become fluent in reading medical terminology.

Atherosclerotic refers to the build up of atheroma, (cholesterol or fat) in the arteries, that leads to the passageway through the artery becoming narrow.

Calcification is the build up of calcium, causing the artery to harden.

Intracranial means within the cranium (Skull).

Internal Carotid Arteries are major arteries that supply the brain.

So this phrase means, there are fat and calcium salt deposits within some major arteries to the brain, that have caused the arteries to become more narrow and harden.