Well for clarity, Dim Mak uses the same principles as TCM, namely the manipulation of flows of energy through the body via well positioned application of external force or the practitioner's inner energy(commonly known as qi or ki). However, Dim Mak is NOT TCM, as it is almost entirely practiced by martial artists.
At the low and realistically possible level, the practicioner strikes nerve points to cause numbness or pain. This is used by lots of martial arts, and incorporated into joint locks and nerve strikes.
At the common wuxia level, this expands the numbness to paralysis or unconsciousness, allowing the practitioner to paralyze a subject with a few quick strikes , or against more skilled opponents, merely disable a limb. Very popular with taking people of the the picture, but powerful opponents can regulate their own ki to get around it or are simply too tough to easily stop. This is generally what the 'touch of death' that most people refer to.
At the high wuxia level, this becomes more exaggerated. You can induce(by injecting conflicting ki) or purge poisoning, strengthen or weaken muscles by unlocking channels, send people into comas(including yourself, or feigning death) or crush internal organs. The touch of death is amongst these, by striking a point that causes fatality.