Cutscene diving allows you to reach the bottom of a body of water, usually Lake Hylia, without using the Zora Armor. In an Any%, cutscene diving is especially useful, as well as crucial, for entering Lakebed Temple without the Zora Armor.
On the Wii version of Twilight Princess, using an item to push you off of a ledge, most often a box, while interacting with an item that has a cutscene, is the preferred method of diving. To do this, pick up an object that Link will hold above his head. The most commonly used item is a box. Now get close to a ledge and pull out or interact with an item that has a cutscene. The most commonly used are either a bottle filled with something, or Midna. Interacting with this item will cause Link to drop the object he was holding which will then push him off of the ledge he was standing on; essentially diving off of the item cutscene. The most common use for this trick is Midna Diving into Lakebed Temple on the Wii version.
Though you cannot use the traditional item push dive on the GameCube version, there is another way you can use an item to push you into a dive by interacting with someone's text. To do this, pick up an object that Link holds above his head and get in front of a person with a ledge very close behind you. (There are not many locations where you can do this.) Now talk to the person and you will set down the box and be pushed off the ledge by it. Because of the perfect circumstances and environment you need to preform this trick, it is seldom used in a speedrun even though it is easier to do than rupee dive.
Unlike the previous method, this type of diving can be done on all versions of the game. To do this, locate a Rupee that has a value higher than 1. Now use the Gale Boomerang, sometimes coupled with another object, to move the rupee just on the very edge of a platform. Now use either a jumpslash or a spin attack to collect the rupee. If done correctly you will grab the rupee as you fall off of the ledge and dive off of its cutscene. This method is much harder to do than the previous method and is hardly ever used on the Wii version. You must also make sure that you have not already grabbed a rupee with a cutscene before attempting to dive, or the cutscene won't display. The most common use for this trick is diving into Lakebed Temple on the GameCube version.