To taper is to gradually grow smaller or more narrow or less intense. Taper is often used with the word "off." Part of the power of the Vietnam Veterans Memorial is how the two walls appear to taper off into infinity.
As a verb, taper can refer not just to physical objects that narrow: the weather forecast might call for heavy snow that will taper off at the end of the day, and public interest in a political scandal might taper off over time. As a noun, taper refers to a shape that narrows at one end, and it's also another word for a candle that is smaller at one end than the other. "Narrow candle" is the original meaning of the word, and it seems to derive from the Latin papyrus, which was once used to make candle wicks.