“hyperintense lesions” basically means white spots. Scanner signal is translated into a gray scale to form the images. The higher the signal, the paler / brighter that area shows up on the image and the lower the signal, the darker the area. On the type of scan that is good at showing demyelination, lesions give a high signal so they look pale and stick out against a darker background. Hyperintense just means very bright.
The brain is divided up roughly into the cerebrum (the big part on the top), the cerebellum (the smaller round part underneath and towards the back of the cerebrum) and the brain stem (which is in front of the cerebellum and goes from the cerebrum to join the spinal cord). The “tentorium” is a kind of membrane that separates the cerebrum from the cerebellum. “Supratentorial” means above the tentorium, therefore the cerebrum. “Infratentorial” means below the tentorium, so the cerebellum (and the brain stem).
So basically you have lesions in the cerebrum, the cerebellum and/or the brain stem, and in the upper spinal cord.
He might not calling it MS because there are other kinds of demyelinating diseases. Hopefully your other test results as well as your clinical exam and symptoms will complete the puzzle for him and you won’t have to wait too long for a diagnosis.