SSM reaction is a solid state combustion synthesis. Usually the reactants in this kind of process are chosen such that one of the products (preferably one of the side-products) has a very high lattice energy and its formation provides the "driving force" for the reaction. An example is:
5Li3N + 3TaCl5-> 3TaN + 15LiCl + N2
In this case the desired product is TaN and after that LiCl may be removed simply by dissolving in water.
Usually SSM methods are preferred because they are easier to control than the other widely used solid state combustion method SHS (self- propagating high temperature synthesis, e.g. the "thermite process") and this way you can control morphology. For example you can prepare carbon nanotubes by using SSM in just a few seconds.
You can use it to produce all kind of compounds like nitrides, oxides, silicides, sulfides, phosphides and etc.
This information is taken from "Solid state chemistry and its application" by Anthony West.