Tvak names the skin in ordinary Sanskrit, and the Samkhya tattva that carries the name is, characteristically, not quite the same thing as the organ a physician would describe. The gross skin is where touch happens to be located, extended across the whole body rather than confined to a point the way sight is confined to the eyes, but the tattva tvak is the subtler capacity for registering sparsha, tactile quality, that the skin houses rather than constitutes. This distinction between a gross physical organ and the subtler tattva that actually does the perceiving runs through all five Jnanendriyas, and tvak is a clean case of it precisely because the skin's coverage of the entire body makes the gap between organ-as-location and organ-as-faculty unusually visible.
Tvak is produced, with the other four Jnanendriyas, from the sattvic aspect of ahamkara, and its single tanmatra, sparsha, is understood in the classical system as including not just contact itself but temperature and texture, everything ordinarily grouped under the sense of touch. Later traditions built extensively on this scheme; Ayurveda, for instance, treats the skin as diagnostically significant precisely because it is the seat of a sense organ tied so directly to one of the five fundamental subtle qualities.
Tvak's place in the evolutionary sequence, second among the five tanmatra-linked organs in most orderings, tracks sparsha's own position as the second tanmatra, one step denser than shabda and one step subtler than rupa, form. The ordering is consistent throughout Samkhya's scheme: subtler qualities and their corresponding organs precede grosser ones at every stage.