When the displacements of individual waves combine so as to cancel one another, the result is a small (or even zero) amplitude. This is known as destructive interference.

Again, look at two pulses traveling in opposite directions along a string. One pulse has a +y displacement, the other -y. When they come together they cancel, at least partially.

Once again, after they pass the pulses travel as if they had never met one another.

The actual string is shown at the bottom in purple. Pulses moving to the right are shown in red, and pulses moving left are shown in blue. What the actual string does is the superposition of the top two pictures.