"Ar ôl i mi godi."
Translation:After I got up.
North Welsh î is a "normal" i in most European languages (would be "ee" in English though), whereas north Welsh û is an i-sound with the tounge raised almost to the top of your mouth (the same sound exists in northern west coast Swedish as well, sometimes known as "fisherman i").
As for why the letter is called i-dot: in South Wales, i and u are pronounced identically, so calling them both /i/ would not be helpful :)
So they can be distinguished as "the /i/ sound that's written with a dot on the letter" (i-dot) and "the /i/ sound that's written with a letter shaped like a horseshoe" (u bedol; pedol is a horseshoe).
Khmer and Thai do something similar, distinguishing letters pronounced identically (that are in the alphabet for - how else could it be - historical reasons) by adding a word that starts with that letter, e.g. in Thai, cho chang is "the letter pronounced /ch/ that's used to spell the word chang ช้าง 'elephant'", i.e. ช, as opposed to the letters pronounced identically that are used in the words for "plate" (จ), "cymbals" (ฉ), or "tree" (ฌ).
Wikipedia says that in the north of Wales, the letters i and u are simply called î and û.