Goods are complementary if a reduction in the price of one leads to an increase in demand for the other. They are usually goods that are consumed (used) together, such as gin and tonic or computers and software.
If two goods are complementary, they will then have a negative cross price elasticity of demand.
The sales of some products are sufficiently strongly tied to sales of related complementary goods that it is necessary to model sales of the two goods together.
Some business models exploit the strongly complementary nature of certain pairs of goods, a good example this are razor-blade models.
Complementary goods are the opposite of substitutes: demand for a good will fall if the price of a substitute is reduced.