Drenge (boys, not definite) is pronounced like this, with an audible vowel at the end: http://www.forvo.com/word/drenge/#da
Whereas Drengen (the boy) doesn't have a distinguishable vowel sound at the end, it's hard to describe it, but try listening a few times and comparing Duolingo's pronounciation of drengen with Forvo's drenge
Eventually you will be able to hear the e or the n, it takes a while. That's why i've redone this lesson a kajillion times.
So I guess that the "en" at the end of words stand for the article the? Like Drenge: boy DrengEN: The boy?
yes! En dreng (a boy), drengen (the boy). Danish has two groups of nouns: Some words are "en" words, and some are "et" words. Et hus (a house), huset (the house). Danish speakers just have to memorize them, it gets easier over time.
I think the difference is a glottal stop; if you will, this is how I would write a vocal translation -- 'dreg^n'.
'En dreng' (a boy) becomes 'drengen' (the boy). In Danish the article is simply added to the ending of the word. In some cases, though, it might be only the n (or t), if the word already has an e at the end - like 'en fløjte' (a whistle/flute) or 'et tæppe' (a blanket).