|This article contains something widely considered by /tg/ to be something absolutely disgusting, like pedophilia, rape porn, or any other disturbing topic, like bathing in your allies' blood.|
"In other news, children are getting sexier...and that's pretty cooooool."
- – Tom Tucker, Family Guy
The term loli is used on 4chan to refer to girls who appear to be prepubescent, aka "petite". The word is derived from lolicon, a Japanese term which is itself an abbreviation of Lolita complex. Within the anime fandom the term loli is often used to refer to any girl that meets the aforementioned criteria, regardless of sexualisation or lack thereof. A well-known example of such a loli is Yotsuba, the mascot of 4chan.
Some people contend that using the term loli to describe a character always implies some level of sexual attraction on the part of the speaker, which is false to varying degrees. There are some who also claim that a character's given age can exempt them from loli status (for example, the character Konata from Lucky Star, who is 18 years old but is generall seen as a loli due her design of being short, petite and having a delicious flat chest). Loli is frequently used to also describe pubescent but still underaged girls which is, technically speaking, not correct but most people let it slide as there is no specific term for girls aged 13-17 in wide usage among the anime community (although there is one outside the weeb community: Jailbait). The fact that most artists can draw an adult or a child but many find making teenagers who don't look like either a small adult or a tall child kind of harder to do possibly contributes to this. Ultimately as far as American law is concerned, underaged is underaged whether you're fifteen or eight. Also under American law is that drawings of fictional characters aren't people, since they aren't real and all that (barring tracings). This does not apply in Canada where it's an excuse to be stalling assholes at customs, looking through every page of comics and artbooks to make sure they don't have any loli. The general rule of thumb is someone stops being a loli when they look mature enough to start being described as a woman.
Related to this is the slang otaku term "moe" (萌え, pronounced [mo.e]), which literally means "budding," and a pun on "burning" with passion or light or life. One of the possible origins is believed to be Moe, a loli from the anime 恐竜惑星 (Kyouryu Wakusei lit. Dinosaur Planet) which is rather obscure. This originally described a sort of protective or paternal/maternal instinct invoked onto certain characters. These days it's either used by people to describe girls that are adorable and cute to the point that you want to take care of them.
The rule 63 version of loli is shota, which is typically preferred by either women or extra, extra creepy men (or some very sad men who want to vicariously relive their adolescent fantasies of being ravaged by an older woman). Much like loli, the term shota is also often used to describe pubescent boys rather than just aged twelve and under kids. As with their female counterparts, the dividing line between a shota and a simply young looking man is based on whether you'd probably call the person a boy or a man.
How accepting /tg/ or 4chan as a whole has been of loli and shota has varied quite a bit over the years, though it's worth noting there's always been those who are really into them as well as those who think people into it probably belong in jail. Most of /tg/ falls somewhere between the spectrum with most just choosing to ignore it if they aren't into it. The fluctuations are often caused by the people who are into it migrating onto another image boards, predominately from /b/, /a/ or /c/ (though /jp/ occasionally gets in on the action as well). Though as /tg/ is a work safe board and as of late that has actually started being enforced you're going to be seeing far less loli and shota, at least not any that would warrant bans.
Overall as fetishes loli is certainly on the extreme skub side of things. Sure there are a lot of fetishes that are much more bizarre and esoteric in the "why would anyone think this is hot?" sense as anyone who's looked at /d/ can tell you, but none of them carry anywhere near as much baggage. (Well, aside from furries, but that may not count as furries are historically detested for overlapping and overdoing not directly furry fetishes (e.g. scat, underaged, vore, among others), rather than or in addition to the "bestiality" argument, as well as just plain existing.)
Loli should not (and, indeed, cannot) be confused with Shortstack, the fetish for an adult-figured woman who is much smaller than the typical human man, typically around the height of a child. Indeed, shortstacks often have exaggerated hips, buttocks and/or breasts, which makes them quite visually distinct. "Oppai Loli" is the arguably even-more degenerate offshoot of loli, as it takes a loli character and presents them with adult-sized (and usually exaggerated) breasts on their otherwise childish frame, much to the dismay of many fans of shortstacks.