Anime Fanspeak literally meaning "glasses girl"—one of the classic "sweet girl" stereotypes in anime. The term generally refers to a Bespectacled Cutie character.
When seen through the lens of how attractive others find her, she is cute without going overboard and seems more approachable than a more conventionally beautiful girl. The meganekko is usually pleasant and clever, and something about the fact that she needs glasses seems to imply an endearing vulnerability that makes her far more accessible to the average guy. After the Yamato Nadeshiko, she is presented as the second-best girl that a boy can bring home to meet his parents and probably the more realistic of the two. Naturally, as with any stereotype, the meganekko can be inverted or subverted, but the vast majority in anime are sweet, smart and relatively independent. Occasionally she is an unpopular character within the story, but not with the fans.
The glasses are the important part, though. Whether she's Blind Without 'Em or not, they are presented as key to her appeal. This is one girl who does not need a "Beautiful All Along" transformation; in fact, taking her glasses away is an almost surefire way to reduce her attractiveness! Keep in mind that not all Meganekko/Megane are always nerds or geeks of some sort.
Boys with glasses are called megane, and can occasionally fit into this type (especially in the Yaoi Genre). (Note that boys cannot properly be called "meganekko"; the term refers specifically to girls.)
Compare Speech-Impeded Love Interest, when a speech defect plays the same role in giving an endearing vulnerability to the character.
Pronounced "may-gah-nay-koh", not "MEGA-neko". That'd be a really big cat.
See Bespectacled Cutie for examples.