It's called a dieresis and it comes from French. said AnnaS.

And my Webster's says it comes from the Greek, via that ol' Latin said the pickeur du les nits, overly quickly.

Thinking about this, I miscorrected. While the word diaeresis comes from the Greek, its usage pretty clearly comes from the French, at least in a lot of the diaeresistically-endowed words we've got in English. So correcting AnnaS here was akin to saying the Eiffel Tower ain't French because the word "tower" comes originally from the Latin turris (obviously why so many of 'em go to Eiffel), from the Greek tyrsis.

So, we was both right!