In the Zelda 64 Engine, the physical locations of the game world are broken down into scenes (typically large locations like an entire dungeon, minus boss room), which are then further broken down into maps (the individual rooms of the dungeon).
Almost all scenes contain a number of invisible exit points that link up to other scenes; These exits are part of the scene itself, and can always be tagged to take you to the next scene even if the proper map isn't loaded.
Another important trait of scenes is that the collision mesh for EVERY map is ALWAYS loaded, which means that even if a particular map isn't loaded, the ground/walls where the map should be will be solid.
Now, some scenes hold a collection of similar but disjointed maps rather than one continuous location in order to pack things up neater. With the help of hovering, we can enter a scene with one map loaded, hover over to the area where another map should be, then touch the invisible exit point and end up somewhere else in the world.
There are two important scenes in Majora's Mask where Alternate Exits lead to interesting results.
Fairy Fountains are one of the most common uses of Alternate Exit, since you can warp between Clock Town and the four corners of Termina. The five Great Fairy Fountains are positioned parallel to each other, if you run an imaginary line from the entrance straight through the center of the fountain pool. From right to left, the fountains are ordered as follows: Clock Town - Woodfall - Snowhead - Great Bay - Ikana.
Fairy Fountain Alternate Exit can be done in as little as 8 explosives using the zora long jump to a pillar and 2 megaflips, as shown in the video below.
It is also possible to save an explosive by using a properly angled Zora Jump to grab one of the pillars. Get on one of the ledges nearest the pillar you want to get on top of. Get as close as you can to the acute corner toward the exit and put on the Zora mask. Now do a few double tap punches (ending on Zora Link's second combo punch, rather than two normal punches) to push your way to the very tip of the corner, to the point where it appears that you're floating. Turn around and align the top of the clock with the side of the pillar closest to the center of the fountain and jump. Hold up-left (or up-right) to grab the pillar.
In certain grottos, there will be no physical ceiling around where the light shines down and you can hover out of the room. If you're not sure if a grotto has an open or closed top, aim the hookshot or shoot the bow at the point where the light shines down. If its open, the hookshot or arrow will pass through. When you're out of the room its simply a matter of getting in bounds of another grotto. Here is a map of the grottos:
There are two interesting uses for grotto warping. You can warp to the Lens of Truth cave from a generic pit, and you can Warp to the Deku Palace from the Ocean/Canyon Gossip Stone grotto or Akindo pit.
While it's possible to Alternate Exit in other scenes, it is impractical to do so due to the close proximity of the maps relative to the world. For example, The Zora Hall rooms are all stored in the same scene, but these rooms can be reached quicker by just going through Zora Hall. Romani Ranch's rooms are the same way as well.