Loli is a term derived from the word "lolicon," a Japanese abbreviation of the phrase "Lolita complex," which means a fascination with or fetishisation of underage girls. The phrase is a reference to the novel Lolita by Vladimir Nabokov, in which a man in his late thirties develops a sexual obsession and later becomes involved with a twelve-year-old girl, whom he nicknames Lolita.
A loli can be a cute child, a pre-teen or early-teenage girl, or an older girl who simply appears to be that young, intended to provide fanservice. The character may or may not be depicted engaging in inappropriate behaviour with an older character. The male equivalent is "shotacon" (or, as a character type, "shota"). As one can understand, most Western fans, and most agents, find it unspeakably creepy and squicky. In Japan it's legal as long as it's clearly fictional, and it shows up in some anime and manga, but it doesn't cross cultural boundaries well despite being legal in the US.
Laura of "legolas by laura" may be an unintentional loli, as the author apparently forgot that the character was only supposed to be ten when she made the rampantly OOC Legolas agree to "be her boyfriend." Naruto in "For Your Eyes Only" probably counts as a shota even though he's supposed to be a sixteen-year-old boy, because he behaves and is treated like a stereotypical four-year-old girl... excluding the sex and pregnancy. "Chibiusa's Seventh Birthday" is an example of this in the Sailor Moon fandom.
Not to be confused with lolita fashion, which is a style of dress, also popular in Japan, inspired by Victorian children's clothing. A better description and examples of lolita fashion can be seen here.