A complementary goods is a good whose use is related to the use of an associated or paired goods. Two goods (A and B) are complementary if using more of goods A requires the use of more of goods B.
For example, the demand for one goods (printers) generates demand for the other (ink cartridges). If the price of one goods falls and people buy more of it, they will usually buy more of the complementary good also, whether or not its price also falls. Similarly, if the price of one goods rises and reduces its demand, it may reduce the demand for the paired or complementary goods as well.
In economics, you may often hear about substitute goods. These are the opposite of complementary goods and are a whole other topic by themselves. For instance, Microsoft Windows-based personal computers and Apple Macs are substitutes. If you buy one, you probably don't buy the other. Sprite and 7-UP are another example of substitute goods.