The symbol itself comes from Aristophanes of Byzantium who invented the system of punctuation where the height of placement of a dot on the line determined its meaning. A dot at the top indicated the end of a thought; a dot in the middle indicated the end of part of a complete thought and a dot at the bottom indicated the end of part of a thought. These are roughly equivalent to the period/full stop, semicolon and comma.
The period of full stop is also used at the end of some abbreviations.
Finally 3 dots indicates a continuation, trailing off of thought, the written equivalent of speech trailing off into nothing:
I wonder if...