Destructive Wave Interference  :

When a crest and a trough come in contact and cancel out. The energies combine and work against each other.

Constructive Wave Interference :

When two crests or two troughs from separate sources combine energies to displace the medium. When they both meet the amplitude becomes larger.

Noise cancelling headphones: They use wave interference to eliminate unwanted sound by creating a destructive interference that cancels out the outside noise before in comes in contact with you.