A complementary good is a good whose use is related to the use of an associated or paired good. Two goods (A and B) are complementary if using more of good A requires the use of more of good B.
For example, the demand for one good (printers) generates demand for the other (ink cartridges). If the price of one good 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 good rises and reduces its demand, it may reduce the demand for the paired or complementary good 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.
Examples of Complementary Goods
When you go to Best Buy to get a new computer, what usually happens? You end up buying some software or programs to go with it. You might find out that you need Microsoft Office or specialized accounting software for your business. The new computer alone won't get the job done; you need the complementary software also!