A differential is the price of a physical grade minus its benchmark. It is how essentially all physical crude trades, and it is where the real information about a barrel lives. The benchmark carries the level; the differential carries everything specific.
A differential compensates for three things at once, which is why it is harder to read than it looks. Quality, meaning the value of the products the grade actually yields. Location, meaning the freight from where it loads to where it is wanted. And timing, meaning the loading window relative to the benchmark's pricing window. Reading a differential move as a pure quality signal, when freight moved, is one of the standard errors.
Differentials are also where the refinery connects to the crude market. A refiner is not buying crude, it is buying a yield: a specific slate of products it can make from this barrel with the units it has. When product cracks shift, the relative value of a heavy sour grade versus a light sweet one shifts with them, because the products they favour have repriced. A differential is thus partly a derivative of the product market.