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Super deformed or SD is a specific style of Japanese caricature where characters are drawn in an exaggerated way, typically small and chubby, with stubby limbs and oversized heads, to make them resemble small children. This style forms an integral part of what Japanese and American anime fans refer to as chibi.
Japanese media 
It is often also used on anime and manga in brief interjections to show an extreme or exaggerated emotion, such as anger or surprise, that would be difficult to portray or would seem out of character if expressed on a more realistic face. They are meant to be cute and are often used in humorous diversions from the storyline.
American media 
Americans have used this on several American anime TV shows like 2005's most popular TV series Avatar: The Last Airbender (Super Deformed shorts only). In the Super Deformed Shorts series all characters are depicted as Chibis, parodying the real series (the deformed shorts were created by the creators of the series) and characters. Like their Japanese counter parts, American anime shares the exaggeration of the characters' looks.
The head of a super deformed character is normally anywhere between one third (1:3 ratio) and one half (1:2 ratio) the character's height, often a golden ratio (38 percent), with the eyes taking up much of the space on the head. Some artists may use alternative proportions. There are other exaggerated proportions (such as the 1/5 proportion, as used by Tales of Eternia, etc.) that are popular in anime, but are not considered SD.
In addition to their modified proportions, super deformed characters typically lack the detail of their normal counterparts. As a result, when a character of average proportions is depicted as a super deformed character, certain aspects of his or her design will be simplified and others will be exaggerated. Details such as folds on a jacket are ignored, and general shapes are favored. If a character has a signature characteristic (odd hair, a particular accessory, etc.) this will typically be prominent on the super deformed version of the character.