In Japanese Slang, a girl who acts (or thinks of herself as) excessivly cute. If you're ever watching Japanese Television and catch a CM with some teenage girl acting like she's four years old and saying "iya!" a lot, the term "burikko" definitely applies.

As far as etymology goes, the verb "buru" (Stem form: buri) means "to pretend", and the suffix "ko" means child.

As slang, the term is fading from the vernacular, but people will know what you mean. Hopefully, the burikko style is fading along with the word.

Also, the kanji I saw used for the "buri" in "burikko" meant, apparently, "yellowfin tuna". Maybe my dictionary is wrong.