The Hall effect is when a magnetic field placed transverse to the current flow induces an EMF in a sample. This Hall EMF is cross-wise to the potential difference causing the current flow. For instance, suppose the current is comprised of positive charge carriers and a battery is connected across a resistive piece of material. In which direction does the current flow through the sample?
The current will flow from high potential to low potential, so it will flow from the plux terminal on the battery, through the sample and to the minus terminal. The current flows from left to right through the sample.
Electrons will actually flow the other way. So while current flows down the potential hill, electrons flow up the potential hill. In the following video, the steel balls represent electrons flowing up a potential hill. In this case, the potential difference is caused by gravity. Notice how the distribution of the steel balls is uniform across the board.