An Ironman is a type of 1-on-1 match where each player controls a team of different characters, fighting each other in a series of a 1v1 matches with one character at a time in a format similar to a crew battle, and concluding when one player has defeated all of the opposing player's characters. The idea behind an Ironman is to test each player's ability to play a variety of characters, rather than only being able to play a single or few characters well as a typical tournament-style match tests. The concept of an Ironman match originated from g-regulate and Overswarm on SmashBoards.
Both players pick a set amount of different characters (typically between 5 to 10 characters, but can be any amount up to the number of available playable characters), with each character having a set amount of stocks, usually based on the game's tournament standard (e.g. in Melee they would have 4 stocks, while in Ultimate they would have 3 stocks). They then pick their opening characters before the battle, and either mutually agree to the opening stage or stage strike among the starter stages to decide it.
When a player loses all of their character's stocks, they pick another character and counterpick a legal stage. The winner of the prior game starts the battle with their character's remaining stocks from the prior game, and therefore self destructs to match their prior stock count before the next game starts proper. An Ironman match ends once one player depletes all of their opponent's stocks for every character, with the surviving player being the winner.
Full Roster Ironman
This type of Ironman is functionally similar to a normal Ironman, but involves the full roster instead of a set number of characters. It is occasionally done as a side-event at some tourneys, one of the most famous instances being Mango and Mew2King's full roster Ironman at Smash the Record. Due to the increasingly larger roster size with each Smash game, Full Roster Ironman matches being done in the Smash games beyond Melee are increasingly rare with each installment even in casual settings; Ultimate for example is currently set to have 88 playable characters after its DLC is finished (86 if Pokemon Trainer is counted as one character), meaning with each character having 3 stocks each player would have 264 stocks (or 258 stocks) total to go through, leading to the match taking several hours at least to finish and potentially lasting longer than the amount of time an entire tournament has available. Conversely Full Roster Ironman matches are at their most popular in Smash 64 and are much more a fixture in its competitive scene than in the other Smash games, as with it having only 12 playable characters a Full Roster Ironman will not require significant time investment and can be finished in around an hour. Within the Smash 64 scene a Full Roster Ironman is also known as a "Twelve Character Battle".
Super Smash Bros. Ultimate added a couple modes that are similar to an Ironman match. First there's Smashdown, where after a character has been used in one game, that character is not able to be chosen again by any player until the Smashdown match is finished. Smashdown continues on until after a set number of games have been completed, with the player that has the most wins being declared the winner, or if the mercy rule is enabled, Smashdown ends when a player has won enough games that it's impossible for any other player to surpass their win total in the remaining matches. Enough battles can be set to have Smashdown involve the entire roster minus the Mii Fighters, replicating a Full Roster Ironman but in a different format that is more practical for a roster of Ultimate's size.
Ultimate's other Ironman-like mode is Squad Strike, that has its own three formats available. The most popular is the "Tag Team" format, where a normal 3 or 5 stock match is done, but with each player's stock being a different character. This more condensed format has made it much more popular than standard Ironman as an actual side-event at tournaments, as it can be run as a normal open bracket that any player at a tournament can partake in and still practically fit into the tournament's schedule. For a more standard Ironman fare, the "Elimination" format is nearly identical, but with the difference being that the winner's damage is carried over into the next match too, with an option to recover a set amount between 0-100 damage between matches instead of being recovered completely, and the mode only supports each player having 3 or 5 characters.
For a ruling specific to Ultimate, with its introduction of clone characters known as "Echo Fighters" that are very minimally different from the parent character they're cloned from, Squad Strike and Ironman events may ban players from using both an Echo and their parent character, as it's an unfair advantage for players who happen to main a character with an Echo, allowing them to essentially use their main twice instead of having to use an actually different character. These Echo bans may not extend to Chrom and especially Ken however, as a significant amount of players believe they're different enough functionally from their parent character to not inherently advantage players that main them, but where the line is drawn varies from tournament to tournament, if an Echo ban is in effect at all.