A player's alternate character (often called secondary character, or shortened to "alternate", "secondary", or "alt") is a character they use often, but not as commonly or as seriously as their main character. Most players stick with one or two main characters, but experienced players can often play multiple characters near the level of their main character. The smasher Mew2King is well known for using the entirety of the Melee cast as seen in his two 26 character crew battle such as vs. Mango at Smash the Record. These alternates are most often used in specific counterpick situations when that character would have an advantage, or where the player's main would have a disadvantage, that would outweigh the loss of skill. For instance, ChuDat in Melee withholds his main Ice Climbers against Peach, a strong counter, instead opting to use Jigglypuff against her, a secondary who matches more evenly with Peach.
Secondaries are also sometimes known as "pocket characters", mainly when it's a top/high tier character a player doesn't really practice with but brings out when the character has a significant matchup advantage over their opponent's character, or after they lose with their lower tier "main". King Dedede in Brawl is known to be a common "pocket character", as he hard counters many characters while having a perceived low learning curve. Meta Knight in Brawl has also gained infamy as a common "pocket character", as his arguably broken capabilities and low learning curve have allowed most players to play him nearly as well as their mains despite lack of real practice with him (or even better if their opponent's character is not well suited to handle Meta Knight). As a result, many high level Brawl players are known to have a "pocket Meta Knight" they bring out in matchups they don't like rather than a specialised secondary character (such as DEHF, who is known to use Meta Knight instead of Falco against the Ice Climbers and Pikachu). "Pocket characters" are known to usually lose however to equivalent or greater skilled opponents regardless of significant matchup advantage, as they're not properly practiced with.
More uncommonly, players may have secondary characters they use not for specific matchup advantages, but for either themed matches (such as Fire Emblem only matches) or to cover stages their main does poorly on or simply when they lose confidence with their main in a match. Vinnie for example, after picking up the Ice Climbers as his main in Brawl, would still occasionally use his former main Mr. Game & Watch when the opponent would counterpick a stage the Ice Climbers do poorly on such as Rainbow Cruise, or after losing a particularly bad match with the Ice Climbers.
Sometimes, secondaries aren't characters a player will use for practical purposes in tournaments, but rather are lower tier characters they enjoy playing but can't play as well as their higher tier main (and thus would achieve the player lesser tournament success). Such characters are often played for fun, to sandbag, in non-standard money matches, and in tier restricted side tournaments. Ally's Captain Falcon in Brawl is one of the most noteworthy examples of a lower tier secondary used for such purposes. Vex is another professional smasher known to have especially competent low tier secondaries in Bowser and Ganondorf.