Smiling Titan

The "Smiling Titan" is the unofficial name of the Titan that was notable for killing Eren's mother, Carla Yeager, during the invasion of Wall Maria.

Appearance
The "Smiling Titan" is tall and is shown to lack intelligence like other Titans in its class. Its main distinguishing feature is its characteristic grinning smile; in which its lips are fixed wide open, exposing its teeth and gums within at all times. In the anime, the white part of its right eye is a luminescent yellow color, reminiscent of heterochromia.

The Smiling Titan has a thin emaciated frame with stocky proportions, in which its ribs are visibly apparent, and it possessed an unusually long neck. It has medium-length dark hair that only barely reaches down its head. Though it is not unlike many other Titans in terms of its instinct to seek out and eat humans, it's been shown to kill its victims before devouring them.

Fall of Shiganshina arc
When the Colossal Titan breached through the walls of the Shiganshina District, many Titans proceeded inside and among such Titans was the Smiling Titan. It embarked inside the town and was witnessed by Eren and Mikasa as they tried to free Carla Yeager under debris. Though Hannes initially came to their aid and decided to face the Smiling Titan, he stood catatonic in fear of its frightening appearance. After Hannes realized that he was too afraid to face it, he opted to take Eren and Mikasa to safety, leaving Eren's mother behind. Afterwards, Eren witnessed the Smiling Titan pull Carla out of the debris, as it proceeded to violently incapacitate her and devouring her thereafter.

During Eren's days while training to enlist into the military, it is shown to have left a traumatizing impact on Eren. This was evident when he was approached by his fellow classmates about his impressions regarding normal Titans,  in which Eren experienced a flashback of the Smiling Titan devouring Carla; associating normal Titans to the trauma caused by the Smiling Titan. He remains silent and is visibly shaken by the thought, until maintaining his composure in front of his classmates and shrugging it off as if he were unaffected by their questions.

Clash of the Titans arc
Five years later, after Eren had already joined the Scouting Legion, the Smiling Titan would appear again before Eren and Mikasa outside the Forest of Giant Trees during the military's pursuit of the Armored Titan. After killing Hannes, who tried to save Eren and Mikasa before they were devoured, Eren "punched" the Titan's hand. Activating powers he did not know he had, Eren seemingly gained control over surrounding Titans. The ones that were under his control proceeded to finally kill the Smiling Titan.

Trivia

 * The scene of Carla Yeager's death is depicted slightly different in the anime and manga. In the manga, the Smiling Titan squeezes her until her spine snaps, making her vomit blood and twitch in its hand before it ate her, whereas in the anime, it simply breaks her spine off-screen with both hands, showing the Smiling Titan biting downwards with blood spraying afterwards.