Why do my headphones not require drivers?
Solution 1:
Drivers are software interfaces between the operating system and the device. They allow indirect but standardised communication. Without it, developers would have to talk to the device directly and write code for every imaginable piece of hardware.
Headphones have no need for such an interface, because there is no communication with the operating system that would require 'translation'. The operating system does not control the voltages on the jack sockets, but instead sends digital audio commands and data to the sound card, which does require a driver. The sound card then performs its magic and transforms the bitstream into an analogue signal, regardless of what headphones, speakers, amplifier, recorder, spectrometer... is plugged in, although they often do check whether a jack plug is present at all.
USB headphones are an exception, as they do not plug into a sound card, but they work on the same principle. The mere difference is that those devices have an embedded sound card communicating with the OS, instead of using one that is already installed on the computer. They do require drivers, but since headphones are quite generic peripherals, chances are the embedded sound card is built for maximum compatibility and uses a standardised protocol for which pre-installed drivers suffice, as is common for mice, keyboards and flash drives.
Solution 2:
If your headphones were USB headphones, they may not require drivers as there is a standard manufacturers can follow so the devices they create do not need additional drivers. This is the same way most mice and keyboards "just work".
If your headphones just use a normal jack, the machine's sound card has a set of controllers that are doing the processing for you, the signal going out to the wire is just an analog voltage driving the speakers in the headphones.