When you have interfering waves with the same amplitude and wavelength, the interference pattern is almost stationary (in one place) which is what a standing wave is. The nodes or nodal points are the points that remain still/at rest during the interference of the pulses.
Destructive Interference is when there is a crest and a trough coming towards each other and their energies work against each other to essentially cancel out. This means that the wave almost disappears where they meet.
Constructive Interference’s occur when two different crests or troughs are coming towards each other and their energies combine to displace the medium. This means that energy is passing through each other and the waves get bigger.
How do noise cancelling headphones use wave interference to eliminate unwanted sound?
Noise cancelling headphones uses destructive interference. They incorporate a microphone that listens to ambient sound and calculates a sound wave that will cancel it out. When that second sound wave is played, because of the destructive interference you get silence instead of noise (although it will not be 100% silent)