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:
Last summer, a coalition of environmental groups around the country sent T.N.C. a letter asking it to reëvaluate support for promoting forestry as a “natural climate solution” and, in particular, to come out against burning trees to produce electricity—the so-called biomass energy that scientists now understand to be a major climate threat and that sociologists know to be a prime example of environmental racism.
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: