To warble is to sing in an uneven, quavering voice. You won't win any singing contests if you warble the songs.
Think of the class of song birds known as warblers. They have great songs, but they don't sound quite human. They trill, whistle, vibrate and constantly change pitch. That's a warble. Done well, a human warble can be as engaging as it is difficult. But an old lady with unsteady lungs and vocal chords may also warble, and it is neither deliberate nor very pleasing to the ears.