"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 pre-pubescent 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 8character always implies a sexual attraction on the part of the speaker, which is false, since we could also say we like Petite woman, is it a crime to like cute girls?. There are some who 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 loli can be 200+ years old, Loli does not describe an age,it describes a body type (Petite and cute). Loli is fairly frequently also used to 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 however is that drawings of fictional characters aren't people, since they aren't real and all that (This does not apply in Canada, where the supreme court can't tell fantasy from reality. Canada use this as 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, an loli from the anime 恐竜惑星 (Kyouryu Wakusei lit. Dinosaur Planet) which is now otherwise obscure. This originally described a sort of protective instinct invoked by 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/ 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 really into it migrating onto another imageboards. Though as /tg/ is a work safe board and as of late that has actually started being enforced you're definitely not going to be seeing any Lolicon or Shotacon on /tg/ anymore.
Overall as fetishes they're certainly the most skub prone of them all. 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.)
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.