From the Super Mario Wiki
Magic Scepters (also known as Magic Wands or Koopa Scepters) are the magic items that the Koopalings stole in Super Mario Bros. 3. They were used to turn Mushroom Worlds' multiple Mushroom Kings into various creatures, usually ones that Mario and the gang usually face. The transformations vary between the NES and remakes. The Koopalings also used the Scepters to shoot harmful projectiles when encountered as bosses.
Magic Scepters, along with the Koopalings, appeared again in New Super Mario Bros. Wii. Their most recent appearances have been in New Super Mario Bros. 2, New Super Mario Bros. U, and New Super Luigi U.
The Magic Scepters are seven magic wands owned by kings which were stolen by the Koopalings. They look like large golden rods with round, dome-shaped gems at the end of them in different colors. The scepters' gems are vividly colored and that is where the power is released from.
The scepters were capable of transforming people into animals/plants, although it is implied that they can also be used to restore them to their original form. In addition, the scepters can also fire three-ring shots/spellballs, or in some cases, summon Candy Rings (Wendy O. Koopa), Spike Balls (Morton Koopa, Jr., New Super Mario Bros 2 only), or circus balls (Lemmy Koopa).
The Magic Scepters first debuted in the game Super Mario Bros. 3, where one of the seven Koopalings steal one of the seven magic scepters from the seven kings and use those scepters to turn the kings into animals (or in the case of the Pipe Maze king, a plant). In the e-reader levels for the GBA remake Super Mario Advance 4, despite the scepters being returned to their rightful owners, Larry, Morton, and Ludwig were shown to wield them in battle again.
In the cartoons, Bowser has used Magic Scepters since The Super Mario Bros. Super Show!. They also had prominent roles in The Adventures of Super Mario Bros. 3, being used to make and solve tomfoolery.
Morton uses his scepter to turn the Mushroom King into a rabbit in the book Leaping Lizards. However in that book the wand's magic only worked one-way, so when Luigi tried to use the wand to reverse the spell, instead of turning the king back to normal it turned him into a giant rabbit. In the subsequent book Koopa Capers, Wendy steals her brothers' scepters in order to combine them with her own using a potion she learned about in Bowser's copy of Reptile Magic and VCR Programming Instructions.
The Magic Scepters were not seen again for some time, as they are peacefully resting in the hands of the leaders of the Mushroom World. Although it is not one of the original scepters, Bowser himself used a special rod known as the Vibe Scepter in Super Princess Peach (which was also supposed to feature the Koopalings). This magical object intensified one's emotions to a powerful degree.
After a long absence, Magic Scepters return in the game New Super Mario Bros. Wii. Once again, they are weapons used by the seven Koopalings to defeat Mario and his friends. As with Super Mario Bros. 3, each Koopaling can generate spells of varying speed and intensity, with the exception of Lemmy and Wendy, who utilize circus balls and glowing rings, respectively. As the Mushroom World and its kings have no bearing on the plot of New Super Mario Bros. Wii, these are likely replicas. The spells emitted by the Koopalings' wands also bear the insignia of the Magikoopas (jets of light with a circle, triangle and square), indicating a probable connection.
Alongside the Koopalings, their Magic Scepters also make a return in the game New Super Mario Bros. 2, where all the Koopalings, with the exception of Wendy O. Koopa use their scepters in combat. In addition, although Lemmy retains his scepter's ability to conjure circus balls, Morton's normal spells are instead replaced with conjuring spiked balls in his fight with Mario. All the Koopalings used their magic scepters again in the final level where they attempt to defeat Mario by turning him into stone and making him fall in lava. The Koopalings eventually utilize their scepters once again near the ending, this time to aid Bowser by having him grow larger, although this also resulted in them being hit by the newly huge Bowser.
The Magic Wands make their return in New Super Mario Bros. U, but only Larry, Iggy, and Ludwig retain them. Larry, as per usual shoots out blue fire with his wand. Iggy, as per usual, will shoot out green fire with his wand, although he will also fire red spellballs that, upon making contact with the magma in his cabin, will summon Magmaarghs. Ludwig fires his regular blue fire spells in threes as usual. However, he also utilized the wand to create two false duplicates of himself. Additionally, the orb of the magic scepters now have purple glow to it whenever each of the three Koopalings are casting their fireballs.