The ellipsis serves two purposes.
1. It indicates where words have been omitted from a longer text.
Example: We the People of the United States ... do ordain and establish this Constitution for the United States of America.
2. The ellipsis indicates a trailing off at the end of a sentence. It's often used this way in dialogue. In the middle of a line, the ellipsis indicates a hesitation, and then the thought continues.
A long time ago in a galaxy far, far away ...
"You can't possibly mean ..."
"I thought ... when he said he'd written the check ... well, that the bill was paid."
The ellipsis places high on Internet lists of grammatical peeves. Many of us don't know how to correctly space ellipses or what to do with them at the end of a sentence. Style guides aren't much help, because they differ in their advice. I favor this guidance because it's sensible and easy to remember: space the dots by replacing the ellipsis with a three-letter word, like "car." There should be a space before and after the word, with no spaces in between. Treat ellipses the same way.
She bought a new car yesterday.
It was frightening ... I couldn't imagine what could be growling at the back of the closet.
If the ellipsis falls at the end of a complete sentence, then end that sentence with a period, insert a space, then insert the ellipsis to indicate where words have been omitted.
Example: We have warned them from time to time of attempts by their legislature to extend an unwarrantable jurisdiction over us. ... We must, therefore, acquiesce in the necessity, which denounces our Separation, and hold them, as we hold the rest of mankind, Enemies in War, in Peace Friends.
To make an ellipsis, type three periods without spaces between them. In Microsoft Word, you can insert an ellipsis by using the "insert symbol" menu.
An ellipsis may not indicate a path to infinity, but it's still a pretty useful punctuation mark.