Within the Zelda Universe it is well established that the Triforce of Power grants great power to its wielder. And although the Triforce of Courage is less clear, it seems to give its holder the ability to destroy the great evil. But almost nothing is ever said about the Triforce of Wisdom, what does it do? Does it grant Zelda any special abilities? (do not cite SSB) Does it make her more wise? etc etc.
In other words, aside from its intrinsic value as part of the Triforce, what good is it?
Back in the TV series(Friday only, replaced Super Mario Bros.), and 2 short comics, each character had their own Tri-Force. Wisdom bestowed great wisdom, and was the reason Ganon kept going after this piece. He had the Tri-Force of Power, which did in fact give him great power, but not the wisdom to use it. It changed him into the Pig-beast form forever. Link actually manages to get the Tri-Force of power, and it both saps Ganon of his powers-he becomes drug-crazed, and grants powers to Link....but starts to change Link into a Pig-beast. Once Link tosses aside the Power(knowing he will become Ganon otherwise), he goes back to normal.
Wisdom grants Wisdom. Power for Power, Courage for Courage. Hold all 3 and you summon captain planet/form voltron-or rather just become omnipotent.
Combining what I know of the Zelda video games and the TV series, it would seem that each Triforce grants general magical abilities.... matter manipulation, enhanced physical and mental abilities, effects on the environment and such. In show, we see Zelda [who seems to share a bond with the magical element] channel its power to create certain magical affects, one example of which creating a staircase in Ganon's underground kingdom.
Concurrently, the Troforces seem to also grant specific abilities based around their particular attributes; in the cartoon, for instance, the Triforce of wisdom would literally speak to the protagonists and advise them in the absolute best possible measures out of a scenario, as well as having some clairvoyant capabilities. The Triforce of Power made Ganon a beast of a wizard [literally and figuratively] as he was able to produce and control a seemingly endless number of monsters to wage war on Hyrule, transform himself and others, manipulate weather, teleport at will and fire amazing bolts of magical energy. No Triforce of Courage was ever seen on the show, but [presuming the show is based in similar lore] even prior to finding the vessel, all Links are born "connected" to it somehow... and one of this Link's defining heroic characteristic is his unflappable courage which can actually verge on arrogance or bravado at times.
In the various games, Link is often titled a "hero" of some aspect [such as Time or Light], and Heroism is often an expression of courage. Considering the trials and battles most Links face from the age of boyhood, one would presume he is quite bold and courageous; this would likely be an innate expression of his triforce attribute. It's basically expressed as such in most games...
"If the heart of the one who holds the sacred triangle has all three forces in balance, that one will gain the True Force to govern all. But, if that one's heart is not in balance, the Triforce will separate into three parts: Power, Wisdom and Courage. Only one part will remain for the one who touched the Triforce...the part representing the force that one most believes in." — Sheik (Ocarina of Time)
"Handed down by the gods of old, this power gave its holder the means to make any desire a reality. Such was the might of the ultimate power that the old ones placed it in the care of the goddess." — Introduction (Skyward Sword)
Each Triforce is said to embody the aspect of the goddess that created it. In wisdom's case, this would be...
"Nayru, the goddess of wisdom... Poured her wisdom onto the earth and gave the spirit of law to the world." — Great Deku Tree (Ocarina of Time)
Essentially, the Triforce of Wisdom "embodies" the essence of it's creator (the Goddess of Wisdom, Nayru). Nayru was said to be "the author of law,", both natural and created, to which all the people and nature of Hyrule ascribe to. Specifically, this Triforce imparts divine wisdom unto its holder, and grants them various untold mystical abilities, including healing others, defensive magic and, presumably, the ability to communicate telepathically. This let's the wielder make proper, fulfilling decisions with great acumen and foresight.This may be some kind of limited omniscience or cosmic awareness.
Traditionally, Zelda is the bearer of wisdom; as such, the essence of Nayru grants Zelda, a myriad of mystical abilities on top of the divine wisdom. In The Legend of Zelda, Princess Zelda splits up the Triforce of Wisdom into eight fragments and hides them throughout the land, fearing Ganon's rule after he steals the Triforce of Power. In that game, collecting the Triforce peieces basically served as a "key" to let Link into the final battle with Ganon.
When the Triforce was split into its three aspects in Ocarina of Time, this "new" Princess Zelda was also imparted with the Triforce of Wisdom. This power seems to have allowed her to disguise herself as a Sheikah named Sheik; whether this was her casting a convincing allusion, or a full on physical transformation is unclear, but my guess would be the latter. Her possession of the Triforce of Wisdom also makes her the Seventh Sage, who was destined to be the leader of them all. The Triforce's power also allows the princess to send Link back to his original time at the end of the game, so it does seem to have some chrono-manipulation ability.
In Twilight Princess, when Zant transformed the kingdom of Hyrule into a world covered by Twilight, the Triforce of Wisdom seems to protect Zelda from becoming a spirit in the world of Twilight, much like how Link was protected by his Triforce of Courage. Later, Princess Zelda transfers her powers to the dying Midna in order to save her, thus allowing the Twili imp to be able to withstand light.
I point this out to show that the specific powers and attributes of the Triforce of Wisdom [and other Triforces] can vary somewhat from game to game, but the overall scope and variety of their magical powers is considerable, regardless. Since they all will always stem from the three Goddesses, this makes sense. The "expressions" of those particular powers, though, would likely vary in context.
