I am a learner too, but here is what I understand it as:
One use of "delle" is "some/some of." "Una" modifies "delle" so that "delle" means "one of." Therefore, "Mangio una delle tue mele" means "I eat one of your apples."
I hope this helped.
un/uno/una all mean "one", but which one you use depends on whether the word is masculine or feminine (un/uno vs una) and if it's a masculine word, whether or not it begins with s+consonant (un vs uno).