When used at the end of sentences, だって often expresses something that has been heard by the speaker. This particular use of だって will always be paired with ん or なん.
As だって is a grouping of the 助動詞（じょどうし） (auxiliary verb) だ, and the 副助詞（ふくじょし） (adverbial particle) って, なんだって primarily expresses the following:
なん - Presents an explanation.
だ - Determines something to be true.
って - An abbreviation of と言（い）って ‘is said’ or と思（おも）って ‘is thought’.
In this way, it translates quite similarly to ‘it is that (A) was said/thought’. Realistically though, it is used in the same way as ‘I heard that (A)’, or ‘it’s thought that (A)’.

• サクラちゃん来年（らいねん）結婚（けっこん）するんだって。うらやましいね。
  I heard that Sakura-chan is going to get married next year. I am jealous, aren't you?
• タケル君（くん）が新（あたら）しいおもちゃが欲（ほし）しいんだって。どうしよう？買（か）ってあげる？
  I heard that Takeru-kun is wanting a new toy. What should we do? Should we buy it for him?
• あの博士（はかせ）は凄（すご）い事（こと）言（い）っているように聞こえるけど、実（じつ）は言（い）っていること全部（ぜんぶ）適当（てきとう）なんだって。
  It sounds like that scientist is saying some amazing stuff, but I heard that everything he says is hot air.
• タクミさんはレスラーみたいな体（からだ）しているけど、好（す）きなスポーツはフィギュアスケートなんだって。
  Takumi-san has a body like a wrestler, but I heard that his favorite sport is figure skating.