The nodes of a standing wave are points at which the displacement of the wave is zero at all times. Nodes are important for matching boundary conditions, for example, that the point at which a string is tied to a support has zero displacement at all times (i.e., the point of attachment does not move).
Consider a standing wave, where y represents the transverse displacement of a string that extends along the x direction. Here is a common mathematical form for such a wave: y(x,t) = A sin(kx) sin(ωt), where A is the maximum transverse displacement of the string (the amplitude of the wave), which is assumed to be nonzero, k is the wave number, ω is the angular frequency of the wave, and t is time.