“Dieresis” [di-ER-əs-əs] is a two-dot mark over a diphthong. A diphthong is a sound formed by the combination of two vowels in a single syllable, in which the sound begins as one vowel and moves toward another, as in coin, loud, and side.
An example is naïve. A dieresis is the reason the word “naïve” is pronounced as two syllables. Without the dieresis, it might be a homonym with “knave”, and he is unscrupulous!
The word comes directly from both the Latin diæresis and the nearly identical Greek “διαίρεσις”, meaning “division” or “split”.