There are two principal and related uses of ellipsis (…), both based on their function to indicate that something has been left out (ellipsis means ‘omission’ in Greek).
The first is what we might call the technical use. Here, ellipsis shows that a specific word or larger portion of text has been omitted from a quotation: ‘I did … have sexual relations with that woman …’ (Bill Clinton, 1998).
Be careful when doing this, as in the Clinton example. There, the second ellipsis marks the missing name ‘Miss Lewinsky’, which hardly needs to be supplied; but the first one radically distorts the (intended) meaning of the original.
Sometimes it’s hard to say whether distortion of meaning through omission is inadvertent or deliberate.
Counsel in a recent New York case received a stern reprimand from the judge where the use of ellipsis looked a lot like making a false statement to the court. The judge threatened the lawyer with a fine for contempt, a public reprimand and possible suspension or disbarment: see Colonial Funding Network Inc v Epazz Inc, 16 Civ 5948 (SDNY, 14 April 2017), Stanton USDJ.
The second use of ellipsis is what might be called the rhetorical, where the writer includes the three periods and lets the reader fill in the blank, or wishes to indicate a pause in thought, an ambiguity. Use this device sparingly (if at all) in formal legal writing – it may suggest too casual a tone, a failure to think something through or a meaning you did not intend.