Tsundere is a slang born on the Internet, and it is a word to describe the nature of female anime or game characters. Tsundere is a word combining two words, "Tsun Tsun" and "Dere Dere". Both terms describe attitudes of a person. "Tsun Tsun" is used for cold/blunt/curt attitude, while "Dere Dere" is used when a person becomes spoony
in front of his/her lover.
(Definition is from the game " Tsuyokisu Cool×Sweet ")
Therefore, "Tsundere" is a female character who is usually cold, but she becomes spoony on her lover. Or, she is cold to the main character at first, but she becomes lovestruck later.