HDW stands for Hyper Dying Will in the anime/manga, Katekyo Hitman Reborn!.
It is a "mode" in which the person in that mode has internal limiters removed; that is, it releases the person's hidden awareness. Unlike Dying Will Mode, which removes external limiters and using pressure during a crisis.
Also unlike Dying Will mode, someone in HDW mode seems incredibly calm, instead of overexcited.
A Dying Will Flame appears on the forehead of the person in HDW mode. A person in HDW mode tends to have irises and pupils that match the color of the forehead flame.
Usually in Katekyo Hitman Reborn! Tsunayoshi Sawada is seen in this mode, although others have entered HDW mode as well.
Giotto/Vongola Primo, the founder of the Vongola (a mafia) Famiglia, has always been seen in HDW Mode in the KHR anime.
HDW is an acronym for Hyper Dying Will. It is a state in which Tsuna from Hitman Reborn goes into where he completes a task as if he is about to die; with his dying will.
Tsuna went into HDW mode to beat the captain of the boxing club.