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A character, often cold and harsh on the outside; but swirling with feelings inside. Much like an igloo, they keep an ice-cold wall, in an ice-cold world; just to protect the warmth inside.
The concept is much more common among more emotionally mature characters like older women or obligatory immortals. They try to hide their emotions, but that doesn't mean they are emotionless.
These type of characters don't often have the outlandish or over the top reactions younger characters may have in anime.
Another term for this kind of character can be "dandere". It means to be calm or to keep one's mouth closed.
Somtimes kuudere characters are confused for being tsundere, the major difference being tsundere are usually more denying and abusive whereas kuudere are simply cold and seemingly uncaring.