Mario
Mario is the titular protagonist of a long-running series of videogames, and is generally regarded as the most famous of all videogame protagonists, if not the very first of them. The Super Mario franchise is vast, covering decades of games, with brief forays into cartoons, comics, and even choose-your-own-path books, but the fundamental plot has remained consistent and he remains a surprisingly well-liked character.
His most ancient backstory, which has technically never been retconned, is that Mario and his less famous brother Luigi are Italian-American plumbers who accidentally stumbled into a dimensional portal whilst trying to unclog a drain. This stranded them in the magical Mushroom Kingdom, which was being invaded by the evil Koopa Kingdom, led by a monstrous turtle-dragon-thing called King Bowser Koopa. Although Mario and Luigi beat up Bowser and rescued Princess Peach Toadstool, the ruler of the Mushroom Kingdom, Bowser vowed revenge, and they found themselves drafted thereafter as the chosen ones of the Mushroom Kingdom.
Fun fact: Mario technically shares a world with Donkey Kong and his Kong clan of apes as well as the witch-battling bear & bird duo of Banjo & Kazooi. O at least has easy access to their world via magical portals.
He is most relevant to /tg/ for the fact that at least two attempts to create a roleplaying game set in the Super Marioverse exist:
Characters
Mario, half-jokingly named "Mario Mario" in the infamously awful 80s live-action movie... yes, that was a thing... is the short but adventurous and heroic plumber turned defender of the Mushroom Kingdom.
Luigi, aka "Luigi Mario", is Mario's quirky younger brother, although taller than his sibling. Luigi is Optimistic like his brother but Compared to Mario, Luigi is more Coward, Silly and Clumsy as well as being prone to bad luck. He's never really managed to get out of Mario's shadow, although at least one of the Paper Mario games implies he goes off on his own adventures, he is an equal adventuring party buddy in the "Mario & Luigi" games series, and he does have his own trilogy of games, "Luigi's Mansion", which revolves around Luigi busting ghosts.
Princess Peach Toadstool is the ruler of the Mushroom Kingdom. Though she has been a playable secondary character in a few games, and did get to be the hero once, she's mostly just your iconic Damsel In Distress. She was originally called just "Princess Toadstool", but nowadays people call her "Princess Peach" instead.
King Bowser Koopa, more commonly known these days as simply "Bowser", is a hulking turtle-like dragon and the leader of his own kingdom who wants to conquer the Mushroom Kingdom. He is shown to have something of a twisted crush on Princess Peach. Like her, he used to be known as King Koopa, but is nowadays just called Bowser. In the game Super Mario Bros. 3, he gained a cabal of elite underlings in the form of seven juvenile Bowser-esque creatures called the Koopalings; these were originally portrayed as his children, a state they continued into the Super Mario World game, but afterwards they were unceremoniously replaced by a mini-Bowser called "Bowser Jr."; whilst the Koopalings would eventually be brought back into canon, they lost their status as Bowser's sons (and one daughter).
Bowsette
Long story short, one of the few good things to come out of the years just prior to 2020 was a Mario meme. After the release of Super Mario Odyssey, which ends with both Mario and Bowser proposing to Princess Peach, only for her to reject them both, a new trailer for an upcoming Mario game revealed a new powerup; the Super Crown, which would transform Toadette into a near-clone of Princess Peach.
Cue one madlad drawing a short comic of Bowser and Mario, humiliated by Peach's rejection, coming up with a new plan; Bowser pulls out a Super Crown, and Mario starts dating Bowser, now a hot half-Koopa half-Peach monstergirl.
The internet exploded over these, and the meme, whilst it ultimately burned out, eventually got so huge that Nintendo put forth an official declaration that they would not be making Bowsette canon. Too late to do anything about the huge array of Bowsette or other Super Crown-transformed fanart, or the Bowsette & Mario webcomic, of course.
Races
Toads: Short, cartoony humanoids wearing mushroom cap-inspired... well, caps. The residents of the Mushroom Kingdom, and mostly a bunch of useless cowards. (Unless this is a 4 player Mario game, in which case one or two of them will join Mario.)
Goombas: Ancient lore is that these were Toads who turned traitor and sided with Bowser when he first attacked the Mushroom Kingdom. For whatever reason, their art style remained with the original "walking mushroom with eyes and a mouth" design whilst Toads got to be humans, and they're basically no longer considered to be the same species. Despite looking a lot like cuter versions of squigs, they're both pathetically weak and actually quite intelligent. Non-evil goombas have steadily become a thing in Mario canon.
Koopas: A race of humanoid turtles who serve Bowser, hence his ancient moniker of "King Koopa". Originally, they were depicted as crawling around on all fours, but Super Mario Bros 3 introduced more humanoid Koopas in the form of the Koopa Bros teams, and as such the Koopas have since changed to be 100% bipedal at all times. The standard Koopa is barely better than a Goomba, but they have lots of elite variants, of which the most iconic may arguably be the original Koopa Bros teams introduced in Super Mario Bros 3 - well, the Hammer Bros and Boomerang Bros, at least; the fireball-tossing Fire Bros never caught on so well, perhaps because they were hidden so late in the game.
Yoshis: Strange creatures that seem to be a mix of a dinosaur or a dragon, a turtle, and a frog. They like to act as mounts for Mario and Luigi. They can use their long tongues to swallow enemies whole. Though alway referred to as male, they are hermaphrodites that lay eggs they can use as weapons.
Boos: Spherical ghosts. In most games they cannot move while you are looking at them because they are shy.
Bob-ombs: Walking bombs. In games in which it matters, it's implied that they survive the explosion, although it takes them a while to respawn.
Bullet Bills: Whether they're actually sentient or alive is arguable, and even then probably varies from game to game, but these guys are somewhat-slow-moving bullets with faces.
Penguins: Usually non-hostile, but not quite friendly either.
Pokey: Wandering Cactuses whose heads are more vulnerable then their bodies.
Various aquatic species: Just about every Mario game has several underwater sections, with their own collection of monsters. Some notables include Cheep-cheeps (enemy fish), Bloopers (enemy octopi), Sea Urchins, and Dorrie, a friendly sauropod.
Various undead species: There are a bunch of monsters who are usually pretty unkillable who are skeletons. Notable cases include Dry Bones (a skeleton koopa), Dry Bowser (skeleton version of Bowser; sometimes a separate character or just a powered-up version of Bowser), and Fish Bone (a skeleton fish)