This entry of the Diccionario panhispánico de dudas explains the uses of the diéresis or crema (the ¨ mark) in Spanish (it is mandatory over a u to indicate that this vowel must be pronounced in the combinations gue and gui, as in vergüenza, lingüística), but it gives no hints on its origin.
I would like to know the historical origin of this sign.
Wikipedia explains it pretty well. It was invented by the Greeks, to mark a vowel that shouldn't be combined with adjacent ones into a diphthong or new sound. With that sense it's been used ever since, even in English (although this usage is almost extint). The word diaeresis means separation; crema comes from trema, which is Ancient Greek for pip (of dice), another name given to this diacritic by the Greek.
