In German, umlauts indicate a vowel sound is pronounced differently than its non-umlaut form. The 'ä' in 'Männer' (men) sounds different than 'a' in 'Mann' (man).
Pro Tip 2/3
Visual Recognition
Recognizing umlauts helps differentiate words that would otherwise look alike. 'Fuß' (foot) versus 'Fuβ' (a Greek letter beta, often mistaken by learners).
Pro Tip 3/3
Not Decorative
An umlaut is not just decorative; it signals important changes in meaning. 'Schon' (already) is different from 'schön' (beautiful).