This page is about a technical term of punctuation. There is a separate page on the use of ellipsis as a technical term in the description of language, particularly in the fields of literary criticism and rhetoric.
In punctuation, ... are known as marks of ellipsis. (In American English, they are more commonly known as suspension points.) The three dots (as they are sometimes called in more colloquial English) are used in academic writing to show that something has been left out. In fiction, they can be used to show a pause, gap or change of direction in the speech or thought of one of the characters.
Some style guides lay down that the marks of ellipsis should be enclosed in square brackets, as in [...]. This is justified as indicating that the three dots are a change made by the present writer in the original quotation. Other style guides say that this is only necessary for the omission of longer parts of the text, for example a paragraph or a psge or more. For writing in an area where this applies, such as an academic department or a journal, omissions of a few words are shown by three points WITHOUT square brackets.