Fighter numbers are a method of identifying and sorting characters in Super Smash Bros. Ultimate.
As explained by Masahiro Sakurai, the numbers order characters based on "the order in which they joined the series". They are ordered in the following way:
The Fighter numbers are used to order characters on Ultimate's character selection screen and promotional material. Mii Fighters are instead shown as the last characters on the selection screen, likely due to their customizable nature. The only major in-game usage of the fighter numbers is that Echo Fighters, due to not having their own fighter number, can be optionally stacked onto the character they are based on in the character selection screens for Vs. Mode, Special Smash (except for Smashdown), Tourney, and Online modes (except for Quickplay).
A similar system is used for ordering stages on Ultimate's selection screen, where all stages are ordered by when they first joined the series (with the exception of stages shared between both versions of Super Smash Bros. 4, which are mixed in with stages from exclusively Super Smash Bros. for Wii U).