Big question. I will try to make a short answer.
.1 Heapdhones are made to a perceived market demand
Always remember, every technical product on the market is a compromise between different requirements. In a market economy this is driven on one hand by the demands from the intended market and on the other hand by the costs of production, development and distribution. There is a difference in requirements between a mostly consumer oriented market (say listening when skate boarding), and professional markets (say hearing spoken word in the cockpit of an aeroplane).
.2 There are many technical solutions
In ear, on ear, around ear, open back, closed back, passive, with electronics, with active noise reduction, ...
.3 There are different sound ideals
Some consumers want as "true" or neutral reproduction as possible, generally implying not adding or removing anything. Other consumers want a specific emotional experience, as example added bass boost.
.4 How to achieve bass boost
Acoustically: modify the acoustic enclosure of the speaker element. It could include resonance chambers or using dampening material to decrease the sound volume of higher frequencys.
In a passive headphone (no electronics), the details of the winding of the speaker element does influence sound.
Electronically: all kinds of variations, from simple RC (resistor + capacitor) filters to sound shaping algorithms running in a microcomputer. Active noise reduction includes a microcomputer with algorithms that could change the sound any way you want.
A side note: if you are interested, do a bit of search for hearing aids. The modern ones are ultra small and can be reprogrammed to cater to your individual needs.