An asymptote is a line that a curve approaches but never actually touches. In mathematics, it helps describe the behavior of functions as they extend towards infinity or near certain points. Asymptotes can be horizontal, vertical, or oblique, depending on the direction in which the curve approaches the line. For example, in the case of the function y = 1/x, the vertical asymptote is the line x = 0, while the horizontal asymptote is y = 0. Understanding asymptotes is essential in graphing functions and analyzing their limits in calculus.