Some characters, particularly video game characters in First-Person Shooters and Adventure Games, have a seemingly superhuman ability to carry incredible amounts of stuff at one time, usually an array of weapons along with a couple hundred pounds of ammunition for each one. It doesn't limit their ability to run and jump and crawl through small spaces at all.
In games, what's more, when you see them during cutscenes in first-person games and third-person games, you can't see where they've stowed these things, even when they're wearing clothes that are more or less form-fitting. It seems they've put them away in the same realm where Hyperspace Mallets are kept.
In practice, a Hyperspace Arsenal serves to reduce the more annoying aspects of inventory management, removing the need to constantly shuffle stuff in and out of your backpack. Some games may choose to restrict inventory for balance reasons: It might upset the difficulty curve if the protagonist can carry around an infinite amount of healing items. This can be more realistic as in Halo's rule of no more than two weapons at once or still kind of exaggerated, as in many Adventure Games' "you can only carry twelve items"-type ruling. The result, more often than not, is the more annoying variety of Inventory Management Puzzle (and often pretty absurd—Bazookas regularly take up as much space as gum wrappers.)
In fandom, this trope is often "justified" with the supposition that the Hyperspace Inventory is actually kept in the character's pants. (This however actually serves to answer exactly none of the objections to the trope.) Some less-than-serious works, such as Space Quest, Simon the Sorcerer or Monkey Island, take this very literally.
The reverse occurs in many text adventures, where (primarily for design reasons) the player character could only carry a specific number of items (often five) at any one same time. Regardless of how large these items are.
One odd effect of the Hyperspace Arsenal is that characters may struggle to support an item that they have "taken out" or "equipped," and they may not be able to wear something at all if they're not strong enough—yet presumably they're carrying this very item around all the time. Put another way, as long as you can't see it, it weighs nothing. (This could mean that the equipment is too heavy to be feasible in battle, though.)
Another odd effect, usually found in Adventure and Role-Playing games, is an inventory limit on a single kind of item. The classic example is being able to carry 99 healing Potions and 99 Antidotes, but not 198 Potions or even 100. Some games have even more stringent limits.
Compare Extended Disarming, which often happens when a character is asked to empty out their Hyperspace Arsenal. Compare also Variable-Length Chain, where chains and whips can "stretch" to attack a far target without being long when unused.
Contrast Walking Armory, where the character is actually shown carrying all of their weapons on their body.
- Seikerin from Rental Magica carries over a dozen polearms under his robes. Considering that they're taller than he is, the number he should be able to carry that way is zero.
- The Batman doll concept art from from Skinpop Studio (lower half of the list). It got sword, telescope, several books, guitar and mini-sofa, among other extras. It's shown to be hollow to contain all this, of course.