in simplest words ever: "timbre" is sound signature / tonality difference between various instruments and quality of its presentation.
For instance, a guitarist solo-ing down to low end to a point where it reaches same pitch as the bass guy. at that time, though same notes are hit. you would still be able to tell the bassist from guitarist. in an extreme example, suppose the guitairst's distort pedal / overdrive / effects creates almost same tonality as bass, at that time a good headphone will still resolve the very very fine tonality difference when same notes are hit on that guitar and its bassist counter part.
And what a coincidence, talking about timbre as I am listening to daft punk's Random access memories through my dubstep and gym headhphones - "The V-Moda crossfade LP2" which is, by far best in the deep, rumbly, almost vibrating in your ear bass department.
Coming back to that track, exactly at 3:43 when classic 80s square wave synth tone mixes into vocoder-ed robot vocal hummings, a good headphone like this will resolve the tonality difference with great detail and separation.
I have literally seen headphones, in the frequency range they are weak at, to screw up instrument timbre and almost echo / muffle up and mess up everything if something really complex is going on in frequency spectrum / region which they are weak at.
some do that in midrange, some in bass, there is not a lot of timbre resolution job at hi-hat / sibliant freqnuencies anyways,, not that i have seem.