Displacement reaction is a process were a single element replaces another compound to form as new compound.
AB + X-----> AX + B
Example: Fe + CuSo4 ----> Cu + FeSo4
In double displacement two molecules in different compounds replaces to form two different compounds.
AB + XY -----> AY + BX
Example: AgNO3 + NaCl -----> AgCl + NaNO3