When an electric current flows through a material, electrons (shown here as blue blobs) move through it in pretty much a straight line.
Put the material in a magnetic field and the electrons inside it are in the field too. A force acts on them (the Lorentz force) and makes them deviate from their straight-line path.
Now looking from above, the electrons in this example would bend as shown: from their point of view, from left to right. With more electrons on the right side of the material (the bottom in this picture) than on the left (the top in this picture), there would be a difference in potential (a voltage) between the two sides, as shown by the green arrowed line. The size of this voltage is directly proportional to the size of the electric current and the strength of the magnetic field.