A dieresis is two dots above the second of a pair of vowels to show that you pronounce each vowel; it’s not a diphthong. Perhaps the most common example is in the word coöperative, or maybe naïve.
Here’s another, from the New Yorker, of course:
Usually people use a hyphen because they don’t know how to make a dieresis. Hence, re-evaluate and co-operative. That’s okay.
here’s a picture of the ASCII codes for the dieresis: