A Star Gem is a rare item in Puzzle & Dragons: Super Mario Bros. Edition that allows the player to "awaken" teammates, allowing them to use Awoken Skills, special Skills that are used automatically in battle (similar to Helper or Leader Skills). Star Gems can be obtained by defeating Gold Goombas or Ludwig von Koopa with a 10+ combo attack (if the latter hasn't already joined the player); can be randomly dropped by Gold Goombas, Roy Koopa or Ludwig (before either Koopaling joins the player); earned by successfully opening ? Blocks under three objectives, or winning them in the Lucky ? Blocks game at Toad Houses after clearing World 6.
Star Gems are redeemed by visiting Tamadra at the Awaken spot in Toad Houses. Awakening a teammate requires a certain amount of Star Gems depending on the teammate, and increasing their Awoken Skill by another level requires more Star Gems than the last. A full list of how many Star Gems are needed to awaken a character, or raise a character's Awoken Skill level, can be found here.