Dilegua means "vanish" or "disappear". It's a more poetic and less common verb than simply saying scomparire.
In the song, the lyric "Dilegua o notte" translates to "Vanish, oh night". The singer is expressing a desire for the night to pass, perhaps to escape the pain or memories it brings, or to usher in a new day. This dramatic plea makes the word stand out.