More common in works revolving around warfare, a Mary Tzu is a character, usually a military commander, with unrealistic tactical abilities. They can pull a win out of any battle no matter how outnumbered, outgunned, or outmatched, can guess any enemy commander's plan no matter how convoluted or how little information they have to work from, and any plan they come up with will work perfectly, often employing Hollywood Tactics, resulting in total enemy defeat and another smashing success for General Tzu's track record. As per the standard Mary Sue traits, such a character is usually treated as a paragon and/or revered by the other characters. Sometimes they come complete with a Big Book of War, possibly self-written.
To be clear, this trope only deals with unrealistically good tacticians. Merely great commanders wouldn't apply, as long as they're fallible, or if they're written well enough to make their victories seem plausible. If it looks like they play Gambit Roulette instead of more sound and realistic plans you've got a Mary Tzu. Another test you can do: Are the character's victories all perfect? Or do they suffer losses and pay prices? Even if there isn't a Gambit Roulette every other victory, having plans that are unrealistically successful, such as losing no troops who were sent in to distract heavy fire, that's also a Mary Tzu.
In some respects, one could argue that this is a case where "show, don't tell" does NOT apply. If a character is simply described as an excellent commander, but the writer doesn't actually describe the tactics involved, it's a lot easier to accept, since the actual maneuvers can be left to Take Our Word for It.
Sometimes, this character will merely be a plot device, but other times it can be piled onto the Common Mary Sue Traits of your fourteen year old sparkly invincible teenage girl. Those are only worst case scenarios though, as most characters associated with this trope tend to be older men (which sometimes makes them popular despite being invincible).
In Real Life cases exist of brilliant strategists successfully predicting their opponent's plans, only to then dismiss their own prediction as depending on ascribing Mary Tzu-like powers to their enemy, as well as certain commanders having a Marty Tzu status in legend and image if not in actual performance.
Named for Sun Tzu, a Real Life (maybe) Ancient Chinese general whose The Art of War is still used by many militaries around the world and is considered one of the greatest treatises on warfare ever written, as well as Mary Sue, the archetype of the unrealistically perfect protagonist.
Compare to The Chessmaster or The Strategist, which are for masterminds who push, but don't destroy, Willing Suspension of Disbelief. Also see Hollywood Tactics and Idiot Ball as (like all Mary Sue types), a Mary Tzu's main ability is to make everyone else incompetent so that they look good.
No examples please, as this just explains a term.