The video above shows a constructive interference. A constructive interference is when a crest from one end of the slinky meets a crest from the other end of the slinky. This results in a bigger crest to be created.
The video shows a destructive interference. A destructive interference is when a crest and a trough meet, this causes the waves to cancel each other out.
A standing wave is when two waves interact that are the same wavelength and have the same amplitude. The result is a nearly stationary wave.
How do noice-cancelling headphones use wave interference to eliminate unwanted sound?
Noice-cancelling headphones have a tiny microphone located in the earpiece. These microphones are able to pick up on noise and when noise is detected the electronics in the earpiece create a noise-cancelling wave. The noise-cancelling wave goes 180 degrees out of phase with the unwanted noise.