On a color wheel, complementary colors are in exactly opposite positions. For example, blue and orange in the color wheel to the right.
In addition, the two colors should mix to form a neutral color.
Because complements have such a strong contrast they are often used when a vibrant look is needed. Complementary colors should be used sparingly though as they the combination can be overwhelming.
And you probably don't want to use complements for text. It's very difficult to read when a color text is placed on a background of its complement.