Ackerman clan

The Ackerman family is one of several families that live within the Walls. They were traditionally a bloodline of warriors close to the crown, but after refusing to follow the ideology of the First King, they suffered intense persecution from the monarchy that left them on the brink of extinction and currently there are only few living members left.

History
The Ackermans were one of the families that lived in the world prior to the appearance of the Titans. They were acknowledged as a bloodline of warriors close to the crown and acted as the monarchy's right hand entrusted with humanity's survival; probably thanks to the "awakened power" characteristic of them (see Awakened power). Some members of this family survived the predation by the Titans that started more than 100 years ago and moved within the Walls that the First King built to save the remnants of mankind.

After the First King erased the memories of the people inside, the Ackermans were one of the few bloodlines that showed immunity to this mental manipulation, the others being the Asian races and the noble families. However, along with the Asian bloodline, they refused to follow the King's ideology of a world ruled by Titans as the true peace and gave up their status in order to turn their backs on the monarchy. Fearing his inability to control them, the King plotted a persecution against them, bringing both races at the brink of extinction.

At the end, the head of the Ackerman family offered his own life to ensure the survival of the bloodline and was executed. The rest of the generation avoid telling their children about humanity's lost memories in order to protect them from the monarchy's purge. As a result, the following generations grew up without that knowledge.

Nevertheless, not even this stopped the oppression on them, and several generations later the Ackermans were still pursued, with some of them seeking refugee in the Underground City and others fleeing to the mountains at the edge of the Wall.

The human hunting only stopped after Kenny Ackerman met the then King Uri Reiss; with the latter apologizing for the actions of the prior kings, stopping the persecution, and accepting Kenny as his right-hand man.

Awakened power
Along with their military immunity to mental manipulation, a special ability displayed by the three known - awakened - members of the Ackerman family is a kind of "awakened power" not seen in any other bloodline so far. This ability is described by Levi Ackerman as "knowing exactly what needed to be done". Users of this power exhibit physical abilities far above the average soldier, such as great strength, speed, agility, accuracy and coordination.

In consequence, these users are acknowledged as extremely powerful warriors, with Levi being known as "Humanity's Strongest Soldier", Mikasa Ackerman as "The woman worth a hundred ordinary male soldiers" and Kenny Ackerman being considered by Levi as even more dangerous than himself, his stage name "Kenny the Ripper" being a play off from Jack the Ripper as Kenny was capable of killing more than 100 members of the Military Police without being caught.

This power doesn't seem to be present in all members at first, but is activated when they experience certain moments in their life and it remains active for the rest of their life.

The only Ackerman seen experiencing this moment in the main anime so far is Mikasa, who was normal until the age of 9 when three human traffickers kill her parents and kidnap her. After witnessing one of the kidnappers strangling Eren and being urged by her adoptive brother to fight, Mikasa  power is then awakened and she was able to kill the criminal with a single stab from the back that pierced his heart, displaying a level of speed, strength and accuracy abnormal for a girl of her age, with the floorboards snapping under her foot as proof of her immense power.

Levi stated that himself and Kenny also had similar moments that awakened their powers, though the exact circumstances for Kenny are unknown, in the side anime Levi is seen unleashing his powers after witnessing Isabelle and Farlan's death. Mikasa's father has a much more relaxed,cheerful attitude so if the personality changes are true then he must not have awakened his power, also his short screen time doesn't show him using any powers.

Mikasa experienced a drastic change in her personality after that event, going from being a somewhat cheerful girl to a much more serious and focused person, very similar to the current Levi and partially similar to Kenny. However, it is unknown if this change in personality is related to the awakened power or to the trauma of losing her family, but the same experience has happened with Levi from the side story as he was much more forgiving and smiley before his friend's deaths.

Trivia

 * Eren Headbutts Mikasa.png Of the three awakened Ackermans, Kenny, Levi, and Mikasa, only two have ever been shown being headbutted. The first being Mikasa, when she tries to convince Eren she should stay by his side during the Battle of Trost. And the second being Levi, when Keith Shadis tries to display his authority over Levi before they begin the second part of their expedition. It is because of this that certain individuals are exempt from this "rite of passage."
 * The only other person being shown headbutted was Jean Kirstein, when he admitted that he wanted an easy life within the interior as a member of the Military Police Brigade.