In the strictest sense complementary colors are colors that have no common color. In this way they are total opposites. Red, Blue and Yellow are the three primary colors (meaning they are prime -- they start as themselves and cannot be created by being mixed from other colors). Each of the primary colors has a complementary color that is a secondary color (can be mixed with two primary colors). The primary colors (red, yellow and blue) have secondary colors (green, purple and orange) as their respective complementary (or opposite) colors.
Red is only made of red and the complement of red is green which is made of yellow and blue. Yellow and blue have no Red. Red has no yellow or blue. They are opposites with no color in common.
Blue is only made of blue. The complement of blue is orange which is made of yellow and red. Yellow and red (orange) have no blue. Orange and blue are total opposites.
Yellow has purple or violet as its opposite or complementary color. Purple or violet can be made from blue and red. Yellow has no blue and no red and blue and red have no yellow. They are complete opposites and thus are in a complementary color relationship with each other.
On the color wheel the word opposite also works as the complementary colors are directly opposite each other on the color wheel.
When mixed, complementary colors dull each other. When placed next to each other, complementary colors make each other more intense and forthcoming.