To start with, sound requires a medium to travel as it has been shown that it can not travel in a vacuum. Just like every other type of mechanical wave, sound wave travel by transferring energy through a medium by vibrating the particles in that medium. Bone conduction headphones work simply by propagating sound through your bone.
Normally, the sound we ear travel from the outer ear through the ear canal to the eardrum whose vibration stimulates tiny bones in the middle ear that amplify the sound wave and send them to the cochlea from where the signal is relayed to the brain by the auditory nerves for interpretation. In the case of bone-conducting headphones, the entire outer and middle ear is skipped and the sound waves go to the cochlea through the bone.
However, due to the density of the bone and how tightly packed the molecules of solids are in general vibration is restricted which translates to low sound quality. Also because of this, it’s not as loud as a typical headphone will be. In other words, if you prioritize sound quality in your audio then this is not for you.
Nonetheless, bone-conducting headphones are not made to offer the best sound quality. Instead, it is a safe way to listen to music while running or doing something outdoor while being aware of your surroundings. It also works for listening to music in water if its water proof so you can get your groove on while swimming or scuba diving.
Most importantly, this provides an excellent alternative for people with hearing disabilities as it creates an alternative to listen to audio in the absence of none. Considering it rests on your upper cheekbone or behind the ear instead of your pinna/outer ear, it does not interfere with your hearing aid in any way. So the two can be used simultaneously alongside each other without any issue.