One of the reasons these headphones are so popular is that they have been endorsed by many highly respected audio engineers and they've received many positive reviews. The quality is delivered via the 45mm large aperture drivers with their rare earth magnets and copper clad voice coils.
Magnetism is used by these drivers which creates a movement that makes the sound. The neodymium, or rare earth magnets are ring shaped and have a gap which lets the voice coil move up and down. The voice coil becomes an electromagnet which then interacts with the magnetic field that has been created by the permanent magnet below it.
Rare earth magnets are the strongest permanent magnets made from alloys and there are two types, of which neodymium is one. These type of magnets produce the strongest magnetic field possible.
They are able to produce very low and high frequencies which sound accurate plus keep a perfect balance. The range is from 15hz - 28,000hz and is enough to deliver a really good sound. With a low end of 15hz they deliver very powerful bass, some say it's a little too much, but with the popularity of listening to bass heavy music, they fit the bill.
There is an alternative option if you'd prefer a wider dynamic range and that comes from the next model up, the M70X. Their frequency range is from a super low 5hz up to 40,000hz. While this might seem like a big difference to the M50X, it's widely accepted that the average human ear can only respond to frequencies between 20hz - 20,000hz (source). This means the M50X range is ample to deliver an excellent sound for most people and is one reason why they remain so popular.
The Audio Technica ATH M50X Headphones are over the ear and closed back which are the most popular types with DJ’s and in many recording studios. The reason for this is that they tend to be best for noise isolation.
Over ear, closed back are better at keeping outside sounds out and inside sounds in. There is the possibility that this can give a slightly less natural sound although not with the MX50’s as they do let some outside sound in, perhaps because they're slightly more sleek than other over ear types. The other advantage of over ear, closed back is that they produce an excellent range, particularly bass, as already mentioned.
As over the ear or circumaural headphones tend to be larger than other types they can house bigger drivers which will give a better sound. The drivers can be placed at a better distance from the ear to improve sound reproduction.
The stereo imaging and separation is excellent, which isn't always the case with closed backs. The sound reproduced will be much better if it's delivered from a decent amplifier as these headphones do need to have their sound driven properly. While using a device such as a smartphone might be acceptable, it probably won't come anywhere near the quality produced by a good amplifier. No matter how good the headphones are, they can only reproduce from the quality that's delivered into them.