Reputation is a game mechanic of Descenders.
Reputation is the game's scoring system. When the player does various tricks with their bike, like going at high speed, pulling off spins and front/backflips, riding fakie, or other tricks, they will gain a set Reputation amount for each trick. Note that there are diminishing returns for repeating tricks in a single node; hence, it is not advised to repeat only a single type of trick, but rather mix things up with different tricks and variations.
Reputation has 2 main uses - determining which item you get at the end of a run, and determining when you unlock Career-Plus. Outside of that, it is meaningless, other than as an indicator to show how long you've played the game (in the case of Total Reputation).
Only Reputation earned from Career, Career-Plus, or the Daily Challenge, will count towards your total Reputation (and the final value at the end of a run will determine what drop you get, as below). Reputation earned from Free Ride, Mods, and Bike Parks, will not let you acquire any items nor add to your total Reputation.
The following section, lifted from the Items page, shows how the Reputation earned in a single session determines the post-session item drop.
Common Skins (White)
Common skins require 200 rep in a run for a 20% chance, up to 1k+ rep in a run for a 100% chance.
Uncommon Skins (Green)
Uncommon skins require 2k rep in a run for a 20% chance, up to 10k+ rep in a run for a 100% chance.
Rare Skins (Blue)
Rare skins require 10k rep in a run for a 20% chance, up to 50k+ rep in a run for a 100% chance.
Extraordinary Skins (Purple)
Extraordinary skins require 50k rep in a run for a 20% chance, up to 250k+ rep in a run for a 100% chance.