Speech contains the important message. Noise describes the environment, but if it is very strong, it may make intelligibility difficult.
Acoustically, the speech is formed by harmonic waves. Background noise, by inharmonics. Hearing aids are based on this fact to reduce the amplification of noise and increase it in words.
The devices look for the best voice / noise relationship to promote understanding. The noise can not be eliminated because it also provides information, but it must be left to a level that the brain understands easily with the least effort.
The wind is very annoying for hearing aids, but it has until recently been very difficult to solve.
White waves represent the voice. The gray waves the noise
A good hearing aid is capable of reducing the noise signal below that of the voice
Images by the Oticon company