Hammerspace is the notional place that things come from when they are needed, and where they go back to when not. The term was fan coined as the place cartoon characters and anime/manga characters would store the overly-large hammers and assorted weaponry they had a propensity for hitting each other with, especially for comedic effect.
The actual location of hammerspace is very hard to determine. There seems to be a great deal of it behind people's backs and on the opposite side (from the camera, that is) of thin things like lampposts and slender trees. It also hides in people's coats, closets, clown cars, large sacks, and occasionally down their pants.
Further research into the exact location of Hammerspace awaits solution of a few more basic questions. Such as: "What happens when you turn a Bag of Holding inside out?" and "Why is the inside of the TARDIS only thatmuch larger than its exterior?"
It's also referred to as "hyperspace", but that term gets a little confused with the SF term related to Faster-Than-Light Travel (see Subspace or Hyperspace). Just to confuse things further, "subspace" is a word used in Transformers fandom for Hammerspace. It is called "katanaspace" in Highlander fandom, "back pockets" in the cartoon roleplaying gameToon, and referred to simply as "Elsewhere" in the Fantasy Kitchen Sink roleplaying game Exalted.
There are multiple versions, in order of size:
Basic Hammerspace - This version contains only a few things, not because it is limited in capacity, but because that is all it is ever used for - for example a large weapon, or Optimus Prime's trailer. It is usually played for convenience, and most viewers give it a Hand Wave, although there is occasional lampshading.
Game Hammerspace - Used frequently in games - many of your inventory items are much too large or too heavy to be carried normally, and this is where they are stored until they are used. Game Hammerspace may or may not be infinite, depending on whether your inventory has a limited number of items, but it still holds many things without spoiling the lining of your coat.
Infinite Hammerspace - This version is played with a bent towards comedy. It can traditionally hold as much as the joke requires it to hold, may have multiple dimensions to its capacity (eg somebody looking in and finding one thing, closing the 'door' and looking in again to find something else), and often gets larger as the show goes on.
To take even more comedy out of what is already impossible, a character with established access to Infinite Hammerspace may, after packing it full of things, finally fill it up. With Basic Hammerspace, they are more likely to lose access to it for some reason and be unable to retrieve an item.
All Point-and-Click adventure games had this to an extent or another, because of the technical limitations of the medium preventing these games from having the hundreds of thousands of sprites necessary to represent your character holding any combination of inventory items you can have. So it's usually treated humorously instead.
The term "Hammerspace" originated in the Ranma ½ fanfiction community, ironically largely as a result of Fanon, as neither Ranma ½ nor the character most often associated with it (Akane Tendo) exhibited this trope to an excessive degree, though it was present in the source material.
Sub Tropes include:
The GEICO gecko is apparently an expert at using hammerspace; he is shown to be able to hide a cell phone and wallet larger than his entire body on his person, confusing his boss. Further confusing the boss is that neither he nor the viewer sees the gecko produce the items. The cell phone was already on the table and the wallet is seen only after he turns back around after he talks to a waiter.
Cara Confused from the UK's Confused.com ads has been shown to pull various objects from her pocket, including a house! Many people have "confused" this for something dirtier, as the way every instance is animated seems very out of context.
The term "Hammerspace" originated in Fanfic, most likely for Ranma ½, though the effect itself stems back to the earliest days of animation and graphic fiction
Mercury uses and abuses the Keeper's storage ability in Dungeon Keeper Ami to great effect. It can be used to construct complicated machinery and architecture, store spells for later deployment, catch falling minions and deposit them safely, and teleport.
Nanaki (Red XIII) seems to have this in the fic "Courage to Change the Things You Can." It's used as the story's 'real world' explanation for the massive amounts of storage space the game gives you, but no one else understands how he's doing it and whenthe fic's O.C. main character finally gets mad enough about it to demand an explanation Red replies "I understand your confusion. But I like all of you too much to risk making your primitive hominid brains explode from the revelation."
Later hilariously exploited when the characters need to carry a large amount of luggage, so just give it all to the narrator and have him turn into a dog to whisk it all away to Hammer Space.
In James Bond fan film Diamonds Cut, terrorist sniper at the beginning of London scene uses a laser sight. Try as hard as you might, there is no way you’re going to find it on his rifle, probably because the actual effect was obtained through the use of laser pointer.
Homestuck High; Eridan carries a guitar in his pocket. Particularly bizarre in that the canon actually has sylladexes, a form of technology which would actually permit this, but they seem to be absent from the rest of the fic.
Used as a literal Ass Pull in Sherry Vine's and Peppermint's Telephone Parody, where various utensils are pulled out off Sherry's tush... including a ladder!
Thor of Norse Mythology could make his hammer Mjölnir shrink to an incredibly tiny size, and be pulled out of seemingly nowhere, and is perhaps the first user of this trope. Another god owns a ship that he can fold up and stick in his pocket.
In traditional Chinese folklore, many powerful people essentially had sleeves that could store everything. Being trapped in one was generally a sign that you were screwed.
SCP Foundation. SCP-076-2 ("Able") has the ability to pull non-reflective black bladed weapons out of a miniature dimensional rift described as a "small hole in space".
An episode of Monday Nightsaw Triple H, known for carrying around a sledgehammer, facing off with Randy Orton holding a sledgehammer. Orton suggested they both drop their weapons and just go at it like men. Triple H agreed, both men ditched the hammers they were carrying, and then, after stepping into the ring and removing his jacket, HHH pulled another full-sized sledgehammer out from behind his back and proceeded to chase Orton away. Now, yes, the second hammer was concealed behind his back the entire time, held by a special rig, but the fact that someone managed to pull off the illusion of Hammerspace on a live television program was impressive.
Beneath the ring could count, as everything including a kitchen sink has been pulled out from under the ring. Hornswoggle even lives under the ring and apparently, so do a bunch of similarly sized people. At first, it was just a joke by JBL, but then after being sued by Hornswoggle, DX has to go under the ring and not only find a full sized courtroom, but a building! So yes, on WWE shows, under the ring is officially Hammerspace.
In William Shakespeare's Othello, during the eponymous character's final scene, he pulls out weapon after weapon, as if from hammerspace.
Dead Fantasy Part II. Yuna reaches into her clothing and pulls out two ether bottles to revive an exhausted Tifa. They're so large that there's no way they could have fit in her clothing normally.
Ruby is somehow able to hide a combination gun-scythe weapon under her cloak. But even the weapon's collapsible form is this huge bar of metal that should not be able to fit on her fifteen-year-old body without hindering her movement.
Are we talking the Trailer or the series because in the trailer the collapsed form of her weapon is very obviously hanging at the small of her back with Sticks to the Back
There is no way Ren's gun-blades should be able to fit into his sleeves, let alone leave no sign that they're there. Nevertheless, that's exactly what happens.
Professor Ozpin is always seen with either a cane or a coffee mug, never both. The most blatant occurrence is during the show's very first trial which happens on a cliff edge and in the forest below. Ozpin sends the students off while nursing coffee, no cane in sight. Then he's seen monitoring the lesson while leaning on his cane, no coffee mug in sight. Before this event, the fandom already had a Running Gag that the cane and the coffee mug are the same item, morphing between the two states whenever Ozpin Must Have Caffeine. This event gave that gag wings.
Cinder Fall can apparently use her fire powers to summon a pair of blades, which can also double as a bow. There's no indication yet as to exactly what is going on (Cinder has always been something of an anomaly), but her clothes do glow when she summons them.