Constructive Interference:

Constructive interference is when two crest forms from different sources or from each end. this would cause the two crest to collide and when they do, they combine energies causing it to become a bigger crest. In other words, it creates a crest that is equal to the sum of the two crests that end up colliding. But when one big crest separates, it continues how the two crests were before.

Destructive Interference:

Destructive interference is when the crests and a trough interfere with one another. This would cause the energies to combine and working against one another.

How Do Noise-Cancelling Headphones Use Wave Interference to Eliminate Unwanted Sound?

Noise-cancelling headphones have a destruction interference. The noise-cancelling headphones have a microphone inside that will listen to external sounds that could not be blocked passively. The techinical parts inside the headphones will then uses the noise that was inputted from the microphone and it will generate a wave with the same frequency and amplitude as the incoming waves. After, it will send out a 180 degree copy of that wave that was made from the noise. This noise will cancel out each other as a destructive interference.