This is a casual way to pass on information you got from someone else. It's like saying 'I heard that...' or 'Apparently...'. You're not stating a fact you know personally; you're reporting what someone told you. It often carries a tone of surprise, news, or gossip. For example, if a friend tells you that Yamada-san is getting married, you might tell another friend, '山田さん、結婚するんだって' (I hear Yamada is getting married).

The form is a contraction of のだ + って, where って is the casual quotation particle. So んだって is used in everyday conversation and is not appropriate for formal writing or polite speech. In polite settings, you'd use そうです or ということです instead. Also, note that んだって can also be used to ask for confirmation? Actually, it's mainly for reporting, but with rising intonation it can express surprise or seek confirmation, like 'Is that so?'.

A common mistake is to use it when you're the source of the information. If you saw something yourself, don't use んだって. Instead, use んだ or just state it directly.