Ellipsis (plural ellipses; from the Ancient Greek: ἔλλειψις, élleipsis, "omission" or "falling short") is a series of dots that usually indicates an intentional omission of a word, sentence

Ellipsis (plural ellipses; from the Ancient Greek: ἔλλειψις, élleipsis, "omission" or "falling short") is a series of dots that usually indicates an intentional omission of a word, sentence, or whole section from a text without altering its original meaning.^[1] Depending on their context and placement in a sentence, ellipses can also indicate an unfinished thought, a slight pause, and nervous or awkward silence. Aposiopesis is the use of an ellipsis to trail off into silence—for example: "But I thought he was . . ." When placed at the beginning or end of a sentence, the ellipsis can also inspire a feeling of melancholy or longing.
Uses:

Intentional omission by the writer

A slight pause

Nervous silence

An unfinished thought

Aposiopesis (trailing off into silence)

On the Internet and in text messaging[edit]

The ellipsis is a non-verbal cue that is often used in computer-mediated interactions, in particular in synchronous genres, such as chat. The reason behind its popularity is the fact that it allows people to indicate in writing several functions:

• 
  the sign of ellipsis can function as a floor holding device, and signal that more is to come, for instance when people break up longer turns in chat^[9]
  
• 
  dot-dot-dot can be used systematically to enact linguistic politeness, for instance indicating topic change or hesitation^[10]
  
• 
  suspension dots can be turn construction units to signal silence, for example when indicating disagreement, disapproval or confusion ^[11]
  

Although an ellipsis is technically complete with three periods (...), its rise in popularity as a "trailing-off" or "silence" indicator, particularly in mid-20th-century comic strip and comic book prose writing, has led to expanded uses online. Today, extended ellipsis anywhere from two to dozens of periods have become common constructions in Internet chat rooms and text messages.

(wikipedia.org)