Good question and there is a debate among the head-fi community about this subject. Some head-fi'ers believe headphones sound better with burn-in (meaning getting usually between 50-100 hours listening time, it varies) some head-fi'ers believe burn-in is just a myth. it really depends on who you talk to. I personally believe that burn-in does in fact make certain headphones (especially ones with bigger drivers and higher impedance's) sound better. I believe this because sound is basically a pressure wave. Meaning when you get a new set of cans, the drivers (diaphragms) aren't broken in, as pressure waves (sound) move through them, the diaphragms and drivers become more flexible meaning that the more they are able to move, the more pressure waves can be produced, which also means for higher-impedance headphones amps are necessary to drive them so the diaphragms and drivers can move to produce sufficient pressure waves (sound).
Like I said though, it is a debate and a matter of opinion, some believe in burn-in, others do not. I have 6 different pairs of entry-level to mid-level cans, and I switch between them from time to time. When listening to them for over long periods, they seem to sound better, but that is my opinion.
A good example of this for me is the DT 990 Pro's. I was a little disappointed when I first received them after reading all of the positive reviews and looking at the graphs and testing done on them. I thought "what was all of that fuss about?" However having them for over a year now and well over 100 hours listening to them, even after going to my higher-end cans, the DT 990 Pros just sound amazing. That's my 2 cents.