An Ironman is a type of 1-on-1 match in which 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, as standard tournaments don't require players to use more than one character (and indeed most players only use a single character or two in tournaments). 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 each player using the full roster instead of a set number of characters. It is occasionally done as a side-event at some tourneys, the most famous instance being Mango's and Mew2King's full roster Ironman at Smash the Record. This format presides mostly within the original Super Smash Bros. and Melee; in the former it is a regular fixture of its competitive scene and is also known as a "Twelve Character Battle". Full roster Ironmans for the later Smash games are rare even in casual settings due to each game's increasingly large roster size. Ultimate for example is currently set to have 89 playable characters after its DLC is finished (86 if Pokemon Trainer and the Aegis are each counted as one character), leaving each player with 267 stocks (or 258 stocks) if each character is given three stocks; such an event would take several hours to finish at least, and if done as an exhibition within a tournament, it would likely run well past a tournament's runtime.
Super Smash Bros. Ultimate added a couple modes that are similar to an Ironman match. One of the new such modes is Smashdown, in which after a character has been used in one game, that character cannot be chosen again by any player until the Smashdown match is concluded. 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 is impossible for the opponent(s) 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 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 fit into the tournament's schedule. For a more standard Ironman fare, the "Elimination" format is nearly identical to a standard Ironman format, 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 negligibly different from their parent character, Squad Strike and Ironman events (or gentleman agreement between players for casual matches) may ban players from using both an Echo and their parent character, deeming it an unfair advantage for players who happen to be proficient with a character that has an Echo and thus allow them to essentially use their main (or secondary) twice instead of having to use an actually different character they're less competent with. These Echo bans may not extend to Lucina, Chrom, and especially Ken however, as a significant amount of players believe they are functionally distinct enough from their parent character to not inherently advantage players that play them, but where the line is drawn varies from tournament to tournament, if an Echo ban is in effect at all.