Tsuki-uke, the punching block, refers to the defensive applications of hook punches. The punching block is hardest of all karate blocks -- you literally attack the opponent’s limb faster than they can attack you, either leading to their incapacitation, or to the realization that attempting to hurt you is counterproductive.
Like all blocks, punching block is the most effective when coupled with an evasion, usually a inside 7-3. As you evade, simultaneously throw an opposite-side hook punch to the opponent’s arm. Ideally, you will punch the groove between the biceps and the triceps, to temporarily incapacitate the opponent's arm by striking one of the many major nerves which run through that channel.
[Video of a punching block fast and slow, from the front and side]
Since the opponent is committed to attacking, they are unlikely to block this technique -- rarely does one think of blocking a block! The unexpected pain, ideally acts as an atemi, and the reaction to the shock of the impact can off-balance an opponent for an easy follow-up.
Punching blocks are reserved for advanced students, since they require being skilled and comfortable with both evasions and hook punches.