Akiba-kei literally means "Akihabara style," referring to a district in Tokyo filled with stores selling electronics, manga, anime merchandise, and other products designed to appeal to the otaku subculture.
Akiba-kei particularly refers to men in their 20's and 30's who live in or around Tokyo and spend their leisure time in Akihabara. Their interests are particularly focused upon idols, erotic PC games, model figurines and manga. However, occasionally this also refers to young people (often including women) who look like a geek (otaku), even if he or she is not actually one or has never been to either Akihabara or any other 'geek-chic' place. More or less, now Akiba-kei is used as a synonym of 'creepy people'.
It may be used self-mockingly by Akiba-kei themselves or their friends, neutrally by Akiba-kei amongst themselves, or negatively similar to the English term geek; although in wider Japanese culture the term "otaku" is in more common use, and has the generally negative connotation.
The term was popularized in mainstream Japanese culture as a result of the 2005 movie, and subsequent television series, Densha-otoko.