Paintings are objects from Super Mario 64 and its remake that work like portals. They are used to get to the many levels in the game.
Super Mario series
Super Mario 64 / Super Mario 64 DS
Paintings in Super Mario 64 are used to travel from Princess Peach's Castle to the game's many levels, such as Bob-omb Battlefield. Certain paintings are located in special themed rooms (for example Jolly Roger Bay's painting is in what appears to be an aquarium). Most painting frames are yellow, but some of the paintings also have different colors, such as Wet-Dry World's being blue.
Paintings return as portals in the Super Mario 64 remake, serving the same purpose. One noticeable difference is that the Jolly Roger Bay painting is replaced by bubbles, which was the painting that was used in the Japanese version of the original game, instead of a galleon.
Super Mario Odyssey
Paintings return in Super Mario Odyssey. Also referred to as warp holes in this game, they serve the same purpose of acting as gateways to each of the game's playable kingdoms (excluding the Moon Kingdom, Dark Side and Darker Side), but they are not the primary means of traveling to each kingdom. Instead, they are scattered across each location, often in hidden areas. When used, they send Mario into enclosed areas in each kingdom, to collect Power Moons that are inaccessible through regular means. Before the game is beaten, only Luncheon Kingdom's painting (leading to the Mushroom Kingdom) is activated, all others are completely empty.
Paintings also appear in towers and other hidden areas outside Peach's Castle. They transport Mario to tougher versions of the battles against Knucklotec, Torkdrift, Mecha Wiggler, Mollusque-Lanceur, Cookatiel and the Ruined Dragon. When these paintings are used, the level select jingle from Super Mario 64 plays before the rematches begin.
There is also a painting in the Wedding Hall in the Moon Kingdom which allows for Bowser to be fought again. Another painting can be unlocked in the Wedding Hall by collecting all 880 Power Moons in the game (not counting extra ones obtainable by shopping) which leads to a harder version of the Bowser fight.
List of paintings
From the Odyssey, run past the shop and hug the wall on your right. Cascade Kingdom’s painting is in an alcove behind the waterfall.
Warp to either Tostarena Ruins Round Tower and head northeast, Tostarena Ruins Sand Pillar and head northeast or Jaxi Ruins and head northwest. Sand Kingdom’s painting is on the face of a pillar sitting in the middle of the desert next to a bench where you can call Jaxi.
From the Odyssey, turn left and go up the stairs. There’s a pool where a Lakitu is fishing. At the far side of the pool, on the bottom, you’ll find Lake Kingdom’s painting.
Warp to Iron Mountain Path, Station 8 and turn to face south. Jump off the railing and perform a hat jump (ZL, then Y, then hold Y) to reach the raised platform in the middle distance. Keep heading south and hat jump to the right of the second platform. Wooded Kingdom’s painting is on the roof of the structure ahead.
Metro Kingdom’s painting is easy to find. Just head north from the Odyssey, and hop over a short ledge.
Snow Kingdom’s painting takes a minute to find. From the Odyssey, take over the big, blowing cloud called a Ty-Foo. Fly to a brown part of the ice to the right of the Odyssey. Blow the brown part to the other side, hop out of the monstrosity you took over and enter the painting.
You’ll need to defeat Rango to gain access to Seaside Kingdom’s painting. Swim up to and jump into any of the fountains spouting water where the boss used to be. Hop off the platform in the middle and use ZL to descend to the bottom of the water, where you’ll find the painting.
Luncheon Kingdom’s painting is in the far northeast. Warp to the Remote Island in the Lava, and use Cappy to take over the Lava Bubble in the round hole near the flag. Swim to the northeast, and jump onto the island there. Turn right and take the staircase down. At the end of the stairs, you’ll find the painting.
Warp to the Main Courtyard Entrance flag and turn left immediately. Jump down and walk to the back of the building to find the Bowser Kingdom painting.
The Mushroom Kingdom’s painting is located on the ground in the middle of four trees south of the Odyssey.
Luigi's Mansion series
A single painting makes an appearance in Luigi's Mansion, the one Mario is trapped in, which serves as Luigi's primary goal. After Luigi defeats King Boo, Mario is sent through the Ghost Portrificationizer in reverse to return him to normal. Unlike the static images of the Portrait Ghosts, Mario's picture is of him banging on the panel trying to escape.
Mario gets trapped in a painting again in the game's sequel Luigi's Mansion: Dark Moon. Mario's painting is alluded to throughout the game, but is fully revealed during the Secret Mine. After defeating King Boo, Luigi has to use the Dark-Light Device on Mario to get him out of the painting.