1. A fan of something (female) who is obsessed with the said subject to a certain degree (normally unhealthy).
2. A general term for a female fan of something.
A fangirl is a (female) fan of a character from a movie, anime, video game, etc. or a real life actor or singer. Usually they have an obsession with their "idol" and do various activities to show their love for the said idol. Such activities include ranting about them, making shrines or fanlistings, creating graphics (wallpapers, layouts, etc) that feature the "idol", writing fanfics and making fanart. Some also make plushies or collect posters and other merchandise of their beloved idol.
Usually, members of this label are seen as 1) insane; 2) idiotic; or 3) scary.
However, not all fangirls are like this. Quite a few of them are just an average fan of something, and just call themselves such. But, there are three types of commonly seen fangirls:
1) BELOW AVERAGE FANGIRL
This fangirl is the least likely to cause chaos or mayhem, insult or annoy someone else who is not a fangirl (or boy, if they happen to be male). They admit that they have a slight obsession for something/one, and are mature about it. While they might use smilies (XD, XP, ^_^) and occasionally rant, they try not to go overboard about it.
2. AVERAGE FANGIRL
This fangirl is the most commonly seen fangirl across the Internet, and are generally harmless. They are prone to making shrines, annoying people with their "fantasies" of meeting or marrying their idol, bad grammar, and just being immature about the object of their obsession/affection. Many of these also write fanfics, causing such places as fanfiction.net to be cluttered with stories that could use a good editing and rewriting all together. Another common trait about them is their tendency to rant, be easily insulted, and excessively "glomp", squeal and use chat speak in places where it is not appropriate.
3. ABOVE AVERAGE FANGIRL
This fangirl is above the previous fangirl, and has thus let her obsession go beyond healthy levels. They tend to rant a lot more than other fangirls, and are more easily to insult or anger if you tell them that their "idol" is just a two-dimensional character, or someone whom they will most likely never meet. Their fantasies go beyond the fantasies of the "average" fangirl, along with all of their other tendencies. These are the fangirls most dislike and tend to stay away from due to their ability to easily annoy others, and their high levels of immaturity.
Below Average Fangirl: "I like Jack Sparrow a lot - he is just such a cool character! Look at the wallpaper I made featuring a picture of him! What do you think? :D"
Average Fangirl: "I <3 Jack Sparrow! *glomps him* He's so awesome! OMG, you all should like him too! XD"
Above Average Fangirl: "I luv Jack Sparrow sooooo much! We r going 2 get married! I LUV HIM SOOOO MUCH! Stay away! He is mine!"