A speaker/headphone can produce sound with only the wire coming from your computer/phone, a magnet, and the cone. The electricity from the audio cable manipulates the magnetic field in the speaker, causing the cone to vibrate.

So while the audio cable is transmitting electricity into the headphones, it's just wrapped around a magnet instead of having other electric components.

This is a good graphic on them: https://animagraffs.com/loudspeaker/

A microphone is just the reverse: vibrations in the air move the cone and its attached magnet, which induces electrical current in the wire.

If you disassemble a basic set of wired headphones it is literally just a set of wires from the TRS or TRRS plug to a set of speakers.