The Yami Yami no Mi is a Logia-type Devil Fruit that allows the user to create and control darkness at will, making the user a Darkness Human (闇人間,Yami Ningen?). "Yami" (闇) is the Japanese word for "darkness". In the Viz Manga and FUNimation subs, it is called the Dark-Dark Fruit. It originally belonged to Commander Thatch of Whitebeard Pirates' 4th division, but was stolen and eaten by Marshall D. Teach, also known as Blackbeard. This fruit is very "unique" even for a Logia type.
The Yami Yami no Mi is a large, round, light purple fruit made up of many small teardrop-shaped components with swirl patterns, and green leaves sprouting from the top. Its overall shape and appearance closely resembles a pineapple or a bunch of oversized and unusually shaped grapes.
Darkness is gravity! The power to pull everything in... and spare not even a ray of light!... Infinite gravity!
— Marshall D. Teach
The first and foremost strength, as demonstrated by Blackbeard, is that it allows the user to control darkness and its unique property of gravity. The darkness is visually demonstrated by a black smoke-like substance spreading out from the user's body. The darkness is a void that devours and crushes everything. Due to this, the user can absorb physical matter and attacks of any type by sucking it into the darkness. The user can also use this ability to irresistibly pull the opponent to them, regardless of their current state.
The most unique and frightening advantage of the fruit is that the user also has the ability to nullify the powers of other Devil Fruits by simply touching the user and draining them of their abilities. All types of Devil Fruit, be it a Paramecia, Zoan, or Logia, are affected by this, though Logias are most affected as they can no longer become intangible by transforming into their respective element. This nullification truly seems absolute like as though the Devil Fruit users had never gained their powers at all, as shown when Luffy's stretching powers were canceled on touch; this is unlike the effect a body of water or seastone would have, both of which just inhibit a person from controlling their powers, as shown earlier when Luffy was stuck underwater but his neck could still be stretched above the water's surface and that Busoushoku Haki would simply nullify the defensive aspects of a Devil Fruit such as intangibility and the malleability of rubber.
Similar to a black hole, the user can absorb things inside a vortex. It seems that it does not completely compress and annihilate that which is sucked in as an actual black hole would do, but rather creates some form of space where things are stored. Blackbeard was able to suck an entire city into it and, when eventually regurgitated, everything expelled was reduced to scraps but not completely destroyed. The guards of Impel Down that Blackbeard sucked in also survived, although they were heavily wounded and in shock.
When Blackbeard took the Gura Gura no Mi from Whitebeard's corpse via an unknown method, he claimed that, with the power of darkness that "reduces anything to nothingness" combined with the power of quakes which "brings destruction to all", he was truly invincible and the strongest. Also, in the anime Blackbeard claimed that the Yami Yami no Mi is the strongest power amongst Devil Fruits.
The major strength of this particular fruit, the darkness the user turns into that swallows up everything, is also its major weakness. Since the darkness also absorbs attacks, the user of the fruit is still vulnerable to attacks, which do not pass through the darkness they turn into. If they fail to absorb an attack in time, the user can be hurt like any other normal human being or even more, as stated by Teach.
In addition, while the ability to nullify Devil Fruit abilities is very powerful, the user must actually touch and remain in contact with the victim for the effects to remain constant, meaning that if the victim is somehow separated from the user's physical touch they will quickly regain their Devil Fruit abilities. However, it seems this power can be overcome in certain situations. Whitebeard somehow managed to activate his powers even with his hand around Blackbeard's neck, somehow ignoring the nullification of his Devil Fruit powers through physical contact.
It is possible that Whitebeard used his Haki to nullify the effects, but it is also possible that Blackbeard actually has to touch the other user, rather than the user touching him (similar to how Crocodile has to use his right hand to absorb liquid). However, it seems that touching bare skin is not required, as Blackbeard was capable of nullifying Luffy's powers at Impel Down by touching his clothes, overall suggesting that his hand must be touching the person or material on the person for it to work. Nonetheless, considering the aforementioned attraction ability due to his powers, if the opponent is strong enough to break his grip without the aid of their Devil Fruit, they will regain their respective Devil Fruit powers.
Other than that, the user is also affected by the standard Devil Fruit weaknesses.
The fruit's bestowed powers, as used by Teach, have been used so far for mostly combat purposes. He was able to defeat Ace in battle, his former commander, despite Ace possessing the Mera Mera no Mi.
Black Hole (闇穴道（ブラック･ホール）,Yami Ana Michi [Burakku Hōru]?, literally translated as "Dark Hole Path"): Blackbeard spreads his darkness over a large area and, much like an actual black hole, swallows up anything he chooses. When swallowed, the person or object is subjected to a large amount of gravity and crushed, such as an entire village on the island of Banaro. This technique was first seen as it was demonstrated in front of Ace.
Liberation (解放（リベレイション）,Kaihō [Ribereishon]?): Used following Black Hole. Blackbeard expels all of the destroyed remains of what his darkness had swallowed up at once. This is especially good at demonstrating his power. This was first seen being demonstrated before Ace. Though it is unseen as of yet in the anime, Teach foreshadowed that this attack can possibly be used to launch cannon balls and swords like projectiles.
Kurouzu (闇水（くろうず）,Yami Mizu [Kurōzu]?, kanji read as "Dark Water"; phonetically read as "Black Spiral"): Extending one arm towards his opponent, Blackbeard activates the gravity power of his darkness to pull them into his grasp. Blackbeard can then attack them with his massive strength. This move is particularly useful when used in conjunction with the fruit's power-nullifying abilities, since the target could easily avoid it by fighting at a distance from Blackbeard, as Ace attempted. However, this technique has also proven to be a great weakness, as most opponents he draws near him have attacked him while at close range, such as Ace launching two fiery spears into Blackbeard's chest, or Whitebeard slamming his bisento into Blackbeard's shoulder. The name of the attack is also a pun on the English word "close", and it can also mean "black vinegar", a vinegar commonly used in Chinese cooking. This is called Black Vortex in the Viz Manga and simply Vortex in the FUNimation subs. This was first seen being used on Ace in order to grab him.