An "Abnormal" was an uncommon type of Pure Titan which could possess unusual intelligence or perform unpredictable actions.
History: The earliest known Abnormals were the Wall Titans, Eldians that the 145th King Karl Fritz transformed using the Founding Titan. They were commanded into hardening into three concentric Walls in Paradis Island in the year 743.
Story: During the Fall of Wall Maria, An abnormal Smiling Titan breaches through the Walls and headed straight for the Yeager family's house. It was spotted by Eren Yeager and Mikasa Ackerman who attempted to rescue his mother stuck underneath the rubble, Hannes initially attempts to kill the Titan before hes struck by fear, opting to take Eren and Mikasa to safety, leaving Eren's mother behind. Afterward, Eren witnesses the Titan pull his mother out of the debris, as it proceeds to crush her and devour her shortly thereafter.
Trivia: The Nine Titans were considered to be abnormal Titans, but were classified differently after their actual natures and identities were discovered. Abnormals could vary in many ways from normal Titans. This included intelligence, such as that of the Talking Titan, to immense sizes such as that of Rod Reiss's Titan, which stood at twice the height of the Colossus Titan, as well as the Wall Titans that were nearly as tall as the Colossus.
Source: Abnormal, available under CC BY-SA 3.0.