Something that wanes (1) decreases in size, amount, number, intensity, or degree; (2) declines; or (3) approaches its end. Something that waxes does the opposite. It increases in size, amount, number, intensity, or degree. For example, the Earth’s moon waxes for about two weeks after the new moon and wanes for about two weeks after the full moon.
A separate verb definition of wax is to become. This sense of wax tends to appear in specific phrases, especially wax poetic and wax nostalgic.
Examples
Wane
Flu is on the wane in Wales with the number of people becoming ill falling sharply, figures reveal. [Wales Online]
On the flip side, as gay Republican groups have taken off, social conservative groups like the Family Research Council have seen their influence wane. [Washington Post]
Wax (to increase)
But as those children progress through school, they’ll see handwriting wax and wane in use and importance. [Chattanooga Times Free Press]
Wax (to become)
Pardon me while I wax nostalgic for a year that served up a host of delights. [Escapist Magazine]
I write this not to wax poetic about the landscapes we are fortunate to drink in each day, but instead to recognize what binds us together. [Harbor Light]