Essentially, headphones come in two designs. They have either open-back or closed-back design, a feature that emerges as extremely important when it comes to investing in headphones for your auditory experience.
The closed-back design, which is the most common build of headphones, essentially serves a critical purpose i.e. noise isolation. These headphones have ear-cups that are enclosed on the exterior with metal or strong premium grade plastic. This design essentially seals in the music you are listening to and cut's out any ambient noise. For noise cancellation even beyond this, there are noise-cancelling closed-back headphones that are a step more than noise isolation.
With closed-back headphones, you will not hear the external noise around you, making it appropriate for noisy environments in general. Since there is no sound leakage, these headphones allow you to wear them out and about without disturbing anyone around you. If you enjoy uninterrupted and unadulterated intimacy with your music, closed-back headphones are the best for you.
However, the major drawback of closed-back headphones is that they will never be sonically as good as open-back headphones. The reason for this is that, as the headphone drivers move front and back, there are sound waves directed at the internal parts of the cups, thus causing undesirable reflections that hinder the sound. The other drawback of the closed-back design is that it makes the headphone inappropriate to use while running, cycling or walking in a public place. This is because you are isolated from your surroundings, and you may not be aware of things such as a car approaching while taking a walk on the road.
Open-back headphones are the exact opposite of their closed-back counterparts. This design allows air to pass through your headphones, making them breathe and giving you an experience like listening to live music, where you are conscious of the sounds and noises around you. Since the open-back design reduces any reflections from within the housing and improves the airflow for the drivers' free movement, it makes the music sound more natural. It presents an accurate timbre of instruments and also widens the soundstage.
What emerges to be the drawback of such a design is that there is a good amount of sound leakage, making these headphones inappropriate to be worn in public, as they can be outright disturbing to the people around you. But the same feature makes it a great design as on the road, you will always be aware of what is going on. Another drawback is the lack of isolation, letting all kinds of background noise in and hindering a pure listening experience. Open-back headphones are best for leisurely home listening or in a studio for monitoring. You can't record with open-back headphones due to the sound leaking characteristic.
These two fundamentals of a headphone are tremendously important to consider when you are investing in a pair of headphones. You can decide how you want to listen to your music based on the simple design difference we have mentioned here. Both designs are functional in their own right; hence the choice lies with you as an individual and your unique and personal music inclinations.