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What does 'amabile degli angeli' mean? Sweet angels?

"Amabile" is a particular wine, known for its sweetness.
"Degli angeli" translation should be "Angels' "

Amabile degli angeli means literally: lovable/amiable by (the) angels, but since Amabile is capitalized here it is just a brand name: Amabile of the angels. BTW if you want to say: amiable by (the) angels, that is: amabile dagli angeli. "da" is by/from, "de" is of (followed by an article, "of" without any article following is "di"). Amabile means amiable, indeed they are very similar. Un vino amabile=a lovable/an amiable wine (a smooth wine).