Double replacement means a reaction that includes two molecules that each have two different ions. After the reaction, the ions pairs have switched, which is what is shown in the above equation.
A single replacement would be a very simple reactions such as:
2Fe(II)S + Ov2^2- -> 2Fe(II)O + 2S^2-
A decomposition reaction would be shown as this:
2NaCl -(dissolve in water)> 2Na^+ + Clv2^-
A synthesis reaction could be the exact opposite:
2Na^1+ + Clv2^1- -> 2NaCl
I believe this process is called fixation
