Headphone burn in is achieved by taking new headphones and playing a burn in music track at moderately high volume. The burn in track features a full range of frequencies that exercises and breaks in the mechanical parts of the headphones like a new pair of shoes.
There is a lot of debate surrounding the effectiveness of headphone burn in. There is no scientific evidence that indicates headphones sound better after being burned in. Sure, the company famous for its microphones, also makes headphones and says that the optimal audio quality has already been achieved during final testing, and burning in headphones does not change the audio quality.