Anything bolded is anything I added.
On August 19, 2014, a user created a thread on 4chan's /v/ imageboard with a photo containing the character icons of all previous Smash characters and revealed newcomers, asking who people think will get cut. Later on, a different user created another thread, with the aforementioned user's photo, but modified with never-before-seen character icons on most of the unannounced veterans, including Dr. Mario, who was cut in Brawl, along with never before seen icons of new characters that haven't been announced, who were Shulk from Xenoblade Chronicles, Bowser Jr. from the Super Mario franchise, Dark Pit from Kid Icarus: Uprising, and the Dog from Duck Hunt. In addition to this, there was a red X over the veterans without the icons, signifying they have been cut. These cut veterans were Squirtle, Ivysaur, Lucas, Wolf, the Ice Climbers, and Snake. Curiously, while Mewtwo did not have a new character icon, it had a ? over it instead of a red X, leaving its status unknown.
Later in the thread, a second leaker, with the name of "Mother****ing Leaker", (Censoring for the kids) posted two new images, one showing a nearly full view of the Duck Hunt Dog's render, showing it will fight alongside a duck, and the other showing the character select screen containing all the characters implicated in the OP image. A third different leaker would then post five more images, which showed fuller renders of Shulk, Dr. Mario, and Bowser Jr. (which revealed him being inside his miniature Koopa Clown Car), a customisation menu where the player can select either the characters within the game or Miis, and a stage select screen, showing off many stages that have not been announced. After these images were posted in the thread, the "Mother****ing Leaker" (More censoring) would then post a list claiming the following characters to be DLC: Lucas, Wolf, the Ice Climbers, Snake, and the Chorus Men implicated by the Gematsu leaks. However, the leaker would later admit on Smashboards that he made the DLC list up to catch "copycat leaks" and "to have a little fun", but maintained his leaked images were completely real.
After the 4chan thread was closed, a fourth leaker, with the name of MasterLinkX, posted three new images on GameFAQs, which depicted an ingame shot of a team battle with Shulk and Lucina against Ganondorf and Charizard on Yoshi's Island, and the result screen, depicting one of Shulk's victory poses, and a fuller and much clearer shot of Ganondorf's new render.
The supposed source of the images is unknown, as the leakers never disclosed where exactly the images are supposedly from. However they are believed to come from footage that was sent to the ESRB for review in order to decide the game's rating, as P1's username in the images was "ESRB0083", and the lack of a gap between the top and bottom screen images shows they are not being displayed on an actual 3DS unit. (The gap thing was going to be another thing I was going to bring up.)
Interestingly, these images are consistent with a prior prominent leak on Smashboards, known as the "Ninka/Vaanrose leak". (Never heard about it.) Prior to E3 2014, a Smashboards user by the name of Ninka Kiwi posted that he knew a friend who was playtesting Smash 4, though he did not divulge any specific information, other than Mario and Charizard having new palette swaps, with Mario in particular having a new blue costume (which later turned out to be correct). Later on in July, Ninka would come forward with new information, which included the following; Lucas, Wolf, the Ice Climbers, and Snake being cut, while Shulk, Dr. Mario, Dark Pit, Bowser Jr. in the Koopa Clown Car (with all seven Koopalings as alts), (I'd be fine playing as Iggy as long as it said "Iggy Koopa" instead of Bowser Jr.) and the Duck Hunt Dog being new characters. While being initially disbelieved and seen as too outlandish, a friend of Ninka who gave him the information, named Shun, contacted a Smashboard user by the name of Neo Zero, who revealed to him that he got the information he revealed to Ninka from his own friend, and revealed that his friend recreated and posted two of the new palettes on imgur, before E3 2014. (Too many people involved, got confused.) While this was going on, an apparently completely independent source posted a leaked newcomer list on 4chan (containing Shulk, Chorus Men, Mewtwo, Ridley, Dixie Kong, Duck Hunt Dog, and Bowser Jr.), (8 more newcomers before release? (Didn't Sakurai say that we're getting near the end of newcomer videos?) containing the two characters unique to the, at the time, completely disbelieved Ninka leak. In addition to this, a person in the Smash community known as Vaanrose, came forward to Neo Zero that he knew a friend who knew someone who worked at Nintendo of America's offices in Redmond, Washington, who disclosed to him that Robin, Bowser Jr., and the Duck Hunt Dog were playable. With the screenshot proof of prior knowledge of the new palettes, and these new independent sources backing up a completely disbelieved leak, the people involved publicised this additional information legitimising the leak in a thread on Smashboards. (More people, too confusing. uwu)
Since the screenshots were first posted, they have spread to several websites and been the subject of much debate. Many have claimed the images to be falsified, citing the questionable placement of characters such as Yoshi, Dr. Mario, Dark Pit, and Lucina on the character select screen, the lack of separation between returning and new stages on the stage select screen, the similarity of Shulk's face in his render to that of Little Mac in a previous screenshot (suggesting it was used as a base for a photoshopping attempt), and other similar inconsistencies. Those who believe the images to be genuine have pointed out the presence of obscure UI details consistent with those seen in the E3 demo (including a rare graphical glitch on the bottom screen character renders), the inability to source the renders used on the character select screen, the presence of details that were only very recently revealed at the time (such as Meta Knight's new render, which was less than a week old, and Brinstar, which had only been shown half a day prior), and the stage select icon for Tomodachi Life featuring an apartment design that was not present in any past screenshots but appeared at a different angle in an image from Famitsu magazine that came out the day after the leak. Despite heavy debate and analysis by both sides, no one has been able to definitively prove the images to be real or fake, leaving their legitimacy inconclusive as of now. A thread detailing the arguments against the leak, and their counters, is being maintained on Smashboards.
Another point of debate is if the screenshots, if real, depict the entire playable character and stage roster. The seemingly strange placement of certain characters and stages, the conspicuous empty space on both, the lack of heavily implicated characters such as Mewtwo and the Chorus Men, the seeming over-saturation of past stages, and the question mark over Mewtwo in the original leak image lead many people to believe that there are more characters and stages that were not unlocked at the time the screenshots were taken. To compound the confusion, the leakers never stated if it was the full roster or not, with one of them, MasterLinkX, flatout stating on Smashboards that it was not, and the Smashboards mods investigating the leak being unable to come up with a conclusive answer. However, other observers who believe the leak have maintained that it is likely to be the final roster, citing that the character placement is sensible and complete looking, and that MasterLinkX cannot be trusted, as he refuses to give more information, while also having admitted that he attempted to sabotage his leaked images to create doubt in the leak and halt their spread (such as by photoshopping "disabled" in one of his screenshots to read as "disablad"). (If you don't want people to doubt it, don't point out the errors in your OWN picture.)
Video footage consisting of over a minute of total gameplay was leaked onto YouTube on August 25th by a user named Izat True. The gameplay shows the same scene of Shulk, Lucina, Ganondorf and Charizard on Yoshi's Island, as well as several scenes of Bowser Jr. fighting on Battlefield. This confirms at least the information regarding those clips as legitimate and solidifying the claims of Shulk, Ganondorf, and Bowser Jr.'s playability. The screen also transitions to a Home-Run Contest video instantly at one point, reinforcing the claim that the video is captured from video footage submitted to the ESRB for review. The videos of the leaked footage would eventually be taken down later that day due to a copyright claim by Nintendo. Another set of screenshots posted the same day confirmed the leak.