A special color (also seen in-game as a "SP" color) is a unique color obtained by destroying an ace's plane.
These enemy aces are found in the expert and ace difficulties of the games. They are harder to shoot down than the majority of enemies due to their improved piloting skills. Their locations vary, sometimes in the middle of a battle, other times at the edges of maps. Shooting down an enemy ace will unlock their aircraft's paint scheme, and in the cases of Ace Combat Zero and Ace Combat 6, an assault record. Their special paint scheme will then be available for purchase in the game.
Note that each ace is a bit difficult to find. Sometimes, you just have to travel to a certain spot on the map, while other times they only appear in a certain part of a mission, while aces only appear when certain objectives are completed.