From the Super Mario Wiki
Lumas are star-like creatures that first appear in Super Mario Galaxy. Unlike most Stars, they have a rain drop-like shape and come in many colors. They are much like Power Stars, but are more circular and have the ability to talk. The Lumas are all very friendly and assist Mario during his quest. Lumas have the ability to transform, from minor planetoids to entire galaxies, and according to Rosalina, some Lumas can even transform into Power Stars. They call Rosalina their "Mama". Most of them make their home with her in the Comet Observatory, and others live on Starship Mario following their leader Lubba. Their name comes form the Latin word for light, lumen, which is a reference to their future as stars. In Super Mario Galaxy 2, if the Co-Star Luma spins one, it will emit three Star Bits.
Paper Mario featured a similar species, called Star Kids. Like the Lumas, the Star Kids were young stars, who were raised on a special place to become real stars someday. They also possessed magical abilities, like the Lumas, and a very similar, childish behavior. In addition, Blue Lumas look similar to an item in Paper Mario: The Thousand-Year Door called Mini Mr. Mini.
Super Mario series
Super Mario Galaxy
In Super Mario Galaxy, various Lumas appear on the Comet Observatory and in different galaxies, and Mario is accompanied by a uniquely apricot-colored Luma, who was given to him by Rosalina at the beginning of the game. Luma grants Mario the power to do spins. While he is the only cream-colored Luma encountered by Mario, the Luma that transformed into the comet that Rosalina and the Lumas travel is shown to be the same color in Rosalina's storybook's illustration.
Yellow Lumas transform into Sling Stars and Launch Stars and are the most common variety. Red Lumas guard Red Stars. Green Lumas are the guardians of the Trial Galaxies and transform into green Launch Stars and Green Power Stars. Blue Lumas transform into Pull Stars. Pink Lumas transform into pink Launch Stars to get to hungry Luma galaxies. Lumalee, who is a large, light-blue Luma, hosts the Luma Shop. There is also another type of Luma that is pink, known as the Hungry Luma. The last type of Luma is the Lumacomète, which has the ability to move Prankster Comets.
In the end, all the Lumas (including Mario's Luma) throw themselves into the massive black hole created by Bowser's dying sun to neutralize it. However, Luma is reborn and living on a small planet while it is hinted that the other Lumas will be reborn later.
Super Mario Galaxy 2
Lumas also appear in Super Mario Galaxy 2. Some time before the beginning of the game, Bowser attacked Lubba's ship, and many of the Lumas on board fell down to the Mushroom World. A large number of Lumas are shown to reside in Starship Mario, and their leader is Lubba. Hungry Lumas also appear; this time, they ask to be fed both Star Bits and Coins. Like in the last game, Lumas enjoy being fed Star Bits, and may thank the player if he or she decides to shoot star bits at them. There are exceptionally large species of Luma in the Supermassive Galaxy, called Giant Lumas. Additionally, Mario's companion Luma returns in this game; however, Mario doesn't seem to remember him, and he found the baby Luma when he crashed onto the Mushroom World.
Super Mario 3D World
Lumas appear in Super Mario 3D World where they can be seen floating around in the world maps as well as various levels in bonus worlds. Their behavior has not changed from past main series games like Super Mario Galaxy and its sequel.
Mario Kart series
Mario Kart Wii
Mario Kart 8
Although Lumas don't appear physically in Mario Kart 8, a Luma is seen in the logo of "Galaxy Air" and a Luma's artwork can be seen on the back of the Star Cup trophy. Lumas also appear in the scenery of GBA Ribbon Road included in the second DLC pack.
Mario & Sonic at the London 2012 Olympic Games
Yellow Lumas appear in Mario & Sonic at the London 2012 Olympic Games in the Dream Spacewalk event. Here, they aid the athletes in defeating Dino Piranha. They first transform into Launch Stars that send the characters into space. Following this, they periodically appear to create rings that the athletes must all pass through in order to damage Dino Piranha.
In Fortune Street, Lumas appear in the unlockable Good Egg Galaxy board. A Luma can also be a customizable mascot for the player and is unlocked by placing first in all Mario series boards in the Standard Tour.
Mario Tennis Open
A Luma makes its debut as a playable character in Mario Tennis Open. It is a Technique-type player and it can be unlocked by completing level 3 of the Galaxy Rally special game. Its racquet is turquoise with a picture of a Luma on it. Red, Green, and Turquoise Lumas appear in the background of the Galaxy Arena court. Also if the player is playing as Luma while playing the Galaxy Rally game, the opponent Luma will be blue.
Mario Party: Island Tour
Lumas make their Mario Party debut in Mario Party: Island Tour for the Nintendo 3DS. Yellow Lumas populate the space-themed board Rocket Road where players travel from one space to another in small spaceships. One of them is also holding the checkered flag at the end of the board, while another hosts Battle Minigames. Also, when one of the characters reach the finish line and is congratulated by Rosalina, a yellow Luma, a pink Luma, and a blue Luma appear as well.
Mario Golf: World Tour
Lumas made their debut appearance in the Mario Golf series in Mario Golf: World Tour. After players purchase the Star Pack and receive Rosalina as a playable character, Lumas appear alongside her in her post-hole animations. 
Super Smash Bros. for Nintendo 3DS / Wii U
“Rosalina & Luma Launch into Battle!”
Different colored Lumas appear alongside Rosalina as new playable characters in Super Smash Bros. for Nintendo 3DS / Wii U. As a team, a variety of Rosalina's attacks use these Lumas, especially to aid in combo attacks. Lumas have their own HP, and if they take enough damage, they get defeated. Lumas can get defeated by also knocking them off the stage to the point where they cannot recover. After a few seconds, another Luma respawns near Rosalina. If Rosalina gets KO'd, the Luma vanishes and a new one appears when Rosalina respawns. Lumas can attack even if Rosalina is stunned by other attacks such as grabbing, and their attacks depend on what input the player does as Rosalina. Lumas can also be commanded to use attacks at a long range, and if Rosalina uses her neutral special after she uses her neutral special attack, she commands the Luma back to her. Even though Lumas tend to float in midair, in Rosalina's trailer, a Luma can be seen walking up to Kirby after he accidentally crashes onto Rainbow Road.
Mario & Luigi: Paper Jam
Lumas come in a variety of different colors, some of which have abilities to help Mario or Luigi on his adventure.
Official profiles and statistics
Mario Tennis Open
Character Type: Technique
Names in other languages