Prestige skins are a form of in-game achievement that you can gain in several different ways. Getting prestige levels unlocks special skins with lights on the rims and around the cockpit that show off your prestige level.
See the graphic and the explanations below for an overview of the different types.
To unlock Royal skins, place 4th/3rd/2nd/1st and you'll unlock the respective skin for your team and placement.
To level up, get the same placement again with the same animal.
To unlock Season skins, get 1 bronze/3 silver/5 gold/10 author medals (across the current seasonal campaign and all TOTDs of the season) to unlock its respective skin.
Note that TOTD medals count as long as they were driven during the season, no need to get them on the same day of their release.
To level up, get more medals of the same type. Every 3 bronze/5 silver/6 gold/7 author medals, your prestige skin will level up.
To unlock Ranked skins, obtain the rank and you'll get its skin.
To level up, keep the rank for another month.