A universe (also referred to as a franchise, and officially known as a series) is a term used by the Smash Bros. community to collectively refer to all the particular characters, stages, items, music, and other properties appearing in the fighting games that are thematically featured in another game franchise.
These are the video game series and franchises that the Super Smash Bros. games classify as major enough that they assign each franchise its own unique symbol that appears with characters and stages belonging to that franchise. These franchises generally have characters, stages, items, and other properties that all appear in Smash Bros. games as part of their primary content. However, the minimum requirement for a symbol is to contribute one stage or one character to the games, with one notable exception. Universes that only contribute a stage, with the sole exception of Animal Crossing in Brawl, do not get a separate universe listing in the trophies pages and items and spirits are not tagged with the symbol (for example, Golden Hammer is listed as a Mario item and the Rocket Belt is listed under others).
These are the various franchises that have not been recognized as primary universes by any Smash Bros. game, and this is indicated by the fact these franchises do not carry their own universe symbols. As a general rule, such universes lack any playable characters or stages in the games, but if any of the following franchises contribute an item, Assist Trophy, music, or some other minor element to a given Smash game, the game assigns the property and its respective franchise the default Smash Bros. universe symbol. This was changed in Ultimate, where those universes received a new symbol to represent them in the form of an ellipsis. These universes contribute elements to the gameplay itself, i.e. Assist Trophies, enemies, items or attacks.
Many other series are represented in smaller forms, such as moveset elements, background characters, trophies, stickers, spirits, music, Mii Costumes, or "dependent" universes that tie in to major universes but are not represented themselves.