Translation:The evening is long, the night is short.
Probably because of the "and" that you used rather than a comma. Your sentence would translate as, "Der Abend ist lang und die Nacht ist kurz."
Do you always need an article for Abend and Nacht in German? And if so, would it be appropriate to translate the sentence as "Evenings are long, nights are short"?
It's case. "Die" is the feminine nominative. It's used when the noun is the subject of the sentence. "Die" is also the feminine accusative, which is the direct object, or the object that the action/verb is performed on. "Der" is used for feminine dative nouns, as well as masculine nominative nouns. The dative case is used for indirect objects, which is the object indirectly affected by the verb. Also, there are dative propositions, like "mit," "zu," etc., which automatically trigger the dative case, no matter what.
Ex.: "I gave the bottle to the mother."
'I' is the subject/nominative, 'the bottle' is the direct object/accusative, and 'the mother' is the indirect object/dative. In German, it would be:
"Ich habe der Mutter die Flasche gegeben."
(Note the switched word order: 'der Mutter/the mother' comes before 'die Flasche/the bottle.' Also, the 'to' in the English sentence doesn't need to be translated here since it's implied.)
Sorry for the long and detailed and complicated answer. German has a very intricate system. I'm just grateful that English got rid of this system a long time ago.