“Að búa” means “to live somewhere, to reside”. As is common with many verbs, the main vowel changes to something else in other verb forms. Here, the “ú” has turned into an “ý”.

The letter ý ▶ Play makes the exact same sound as the letter í. Similarly, the letter y makes the exact same sound as the letter i. Y and Ý are only retained for historical reasons.