I'll describe this topic... since it figures that you wouldn't know what a Tsundere is. Look, if you really must know, I suppose that I'll tell you. Just... consider yourself lucky that I just happen to have an article handy, o-okay! blushBaka.
Yes. So. The Japanese term tsundere refers to a character who "runs hot and cold", alternating between two distinct moods: tsuntsun (aloof or irritable) and deredere (lovestruck).
The term was originally used to describe characters who began with a harsh outgoing personality, but slowly revealed a soft and vulnerable interior over time. Over the years the character archetype has become flanderized, and is now generically associated with a character who flips between the two emotional states at the slightest provocation.
The tsuntsun can range from the "silent treatment" to "lovestruck kindergartener who pushes you into the sandbox." The reasons behind a Tsundere's behavior vary widely, but usually boil down to the conflict between their feelings of affection towards a love interest, and their reaction to having those feelings.
The Tsundere stock characterization is very popular with writers of Romantic Comedy because the conflicts between the two personality facets can be easily utilized to generate both drama and comedy. It also acts as a source of Wish Fulfillment: specifically, the idea that every independent, hardened and just plain jerkish love interest (male or female) has a squishy emotional centre that will embrace you after you crack the outer shell.
Tsundere can be divided into two main categories, depending on their default mood:
Type A (alias Type Tsun or "harsh"): These Tsundere have tsuntsun as their default mood. It takes someone special to trigger their deredere side. The intensity of the tsuntsun can range from "I must glare and fight my way through life" (Louise of The Familiar of Zero) to grumpy pessimism (Kagami of Lucky Star). It's about which part of the tsundere personality is the public face and which the hidden. If the Tsundere is The Rival, she is more likely to be Type A. Helping a rival out is usually accompanied by a line like "Don't get me wrong, I'm not doing this for you."
Type A can overlap with a Jerk with a Heart of Gold, but usually not. The moods of a Tsundere tend to switch in reaction to the actions of select people or adverse scenarios; the deredere side usually only comes out when someone has acted in a way to trigger it. A Jerk with a Heart of Gold is jerkish in general regardless of whether the other person is mean or nice, and shows their Hidden Heart of Gold only when the situation warrants, regardless of how the other person had been acting. Male characters in particular should be considered for Jerk with a Heart of Gold status, as arguably because of Double Standards, men are generally that instead of tsundere, although the kuudere subtype is more equally split in gender. Oranyan is sometimes used to refer to a male tsundere character - incorrectly since it means the complete opposite.
See also the Analysis page for more detailed information on common "strategies" employed by Tsundere characters, and other, related topics. this site has an explanation on the appeal of the tsundere character.
A common way of showing that a Tsundere has mellowed or has had her heart won over by the Love Interest is to have her shift from Type A to Type B. If her motivations are inquired, she will often engage in a Suspiciously Specific Denial, complete with a Luminescent Blush and total evasion of eye contact (cue the squeaks of Moe).
In addition, there appear to be three major subtypes which while more common with Type-A may sometimes fit with Type-B.
"Wolf-Girl" Tsundere who can't or won't be honest about her feelings, is quick to judge her love interest (or the main character in a harem comedy) badly, and usually pelts him with violence at the slightest provocation, real or imagined. Bonus points if she calls him an idiot for not understanding her feelings outside his earshot. Prime examples are Nana from To Love-Ru, Asuka Langley Soryu from Neon Genesis Evangelion, Fumino from Mayoi Neko Overrun, Naru Narugesawa from Love Hina.
Discipline Tsundere: Usually a fellow student assigned some role of authority, hall monitor, school president, etc. who is rather strict in rules enforcement. She is quick to blame the love interest for breaches of etiquette and tries to punish him for it. This usually surprises him in that he's getting singled out for attention over others. Romantic interest seldom comes to mind as the reason (at least until he gets wind of further evidence). Prime examples: Yui of To Love-Ru, Asuna of Ore Shura.
Tragic Past Tsundere: This poor girl has a Dark and Troubled Past that makes understanding her feelings, let alone expressing them highly problematic for everyone, including herself. As such, approaching her is rather delicate, and if she approaches someone else, expect many misunderstandings good or bad. While violence towards the Love Interest is not required, it often occurs. Prime Examples: Stella Satellizer of Freezing. Yami of To Love-Ru. (Rito has not one or two, but THREE Tsundere in his Unwanted Harem.)
When paired with a Jerk with a Heart of Gold, together they produce Belligerent Sexual Tension. If done poorly, the result is an Unintentionally UnsympatheticJerk Sue. Compare with Well, Excuse Me, Princess!, Jerk Ass, and Jerk with a Heart of Gold. Contrast with Sour Outside, Sad Inside, which shares the spiky exterior but has depression and self-doubt rather than kindness hiding underneath. When Flanderized tends to overlap with Mood-Swinger. Also see Don't You Dare Pity Me! and Anger Born of Worry; both of them likely actions with this character type. Aloof Ally may show the same hot-and-cold behavior but for differing reasons. Shana Clone is a specific subtrope with a particular set of characteristics. Because of their low tolerance for stupidity, they are always Enraged By Idiocy.
Please do not confuse this trope with a Mood-Swinger, who flips between all the emotional states (not just tsuntsun and deredere) and is more of an inherent mental problem encompassing more than just their romantic life. Also don't confuse with Playing Hard to Get, where a love interest deliberately chooses not to reciprocate her pursuer's interest until she's sure he's hooked.
Psychologically, tsundere-like behavior could be an example of "splitting," a maladaptive coping mechanism wherein a person alternately idealizes and undervalues others, including potential romantic partners.
No Real Life Examples, Please!. You're such an idiot that I just had to put in that bloody obvious rule for you! For invoked examples (ex. Tsundere Cafes), those can go to the "Other" category.
You can go back to the main page here, but don't get the wrong idea! I-i-it's not like I'm leaving this link here for your sake or anything, baka!