维吾尔 is a phonetic transliteration of the self-name 'Uyghur' - the characters were chosen for sound, with
维 (preserve),
吾 (we/I),
尔 (you) producing a pleasing meaning of 'preserving unity among us.' Uyghurs are a Turkic Muslim people whose homeland is the
新疆 维吾尔 自治区 (Xinjiang Uyghur Autonomous Region).