In annealing you heat the material to a very high temperature
(In case of Steel above the upper transformation temperature), hold
it and then slowly cool it in the furnace atmosphere itself. This
makes the grain size coarse.
Contrary to this, in normalizing you heat the ferrous material
(as it is only applicable to ferrous materials) and remove it from
furnace and let it cool in the air. So the material becomes hard.
The reason for this being you get a much refined fine grain
structure.