Following are the types of chemical reactions with a brief overview:
1) Combination (Two elements combine to form a compound)
2) Decomposition (A compound is broken into elements)
3) Single displacement (An element displaces an element present in a compound)
4) Double displacement (The elements of two compounds displace each other)
5) Combustion (Burning Takes places)
6) Redox (Oxidation Reduction Reaction)
If you see the given equation, Al is displacing Ni in the compound NiSO4 and taking its place. Ni is set free as a separate element. So this type of reaction is known as Single Displacement Reaction.