Being able to listen to what you will play next in headphones before your audience hears on the main speakers or your broadcast stream it is an essential part of DJing. DJ headphones are generally better quality than typical consumer headphones. Importantly, they are designed to have good isolation, meaning they block outside sound. This allows the DJ to focus on the sound in the headphones better without having to turn up the volume to drown out sound from the monitors, PA system, and chatter. Also, DJ headphones have hinges or flexible headbands that allow the DJ to take off one headphone cup to hear the monitor or PA output better in one ear and compare it to the headphone output in the other ear.
When shopping for headphones, consider how well they isolate sound and their durability. The most frequent places that headphones break are the cable attachment point and the headband. Look for headphones with detachable cables, metal headbands, and other individually replaceable parts. Avoid Bluetooth headphones because these may be unreliable and will always reduce sound quality. Active noise canceling headphones also tend to have worse sound quality than other headphones of a comparable price. DJ headphones with a closed design block out a lot of sound simply by being closed.
Whether to get on-ear or over-ear headphones is a matter of personal preference. Everyone's head is different, so headphones that are comfortable for a friend or a reviewer may not be comfortable for you.
In-ear monitors (IEMs) isolate sound better than headphones but are more expensive. Good DJ headphones can be purchased new for $150-250; IEMs with comparable sound quality cost $350-$1000. They may be a sound investment for musicians who play often in very loud environments to preserve their hearing.