The simple answer is that "des" is "some" and "les" is the plural form of "the." J'ai des livres - I have some books. J'ai les livres - I have the books, Of course, this implies you are talking about specific books. Of course, sometimes "des" is also the contraction of "de + les", as in "la politique étrangère des (=de + les, not "some") Etats-Unis", which means "the foreign policy OF THE United States." Finally the question you ask about why it is "elle me répond avec une grande patience," in truth we do the same thing in English. We do not say "She responds to me with THE great patience." Instead, we say "She responds to me with A great (amount of) patience." In both languages, if you used LA or THE, people would probably think "what specific patience are you talking about?" Hope this answers your question! :)

il faut employer "les" lorsque l'on parle de choses précises que l'on a vu ou que l'on possède il faut employer "des" lorsque l'on parle de choses en générales, que l'on ne possède pas ou que l'on a jamais approché. Amicalement ........ Mario

des when you can't names precisely les when it is a precise subject