Colloquial 'because/after all' used to give a reason or excuse (e.g., 'だって…').
だって、今日は疲れているんだもん。
But I'm tired today, you know.
行きたくないよ。だって雨が降っているんだもん。
I don't want to go. After all, it's raining.
だって仕方ないじゃないか。
Well, there's nothing we can do about it.
Colloquial 'but' used to add an objection or contrast to what was just said.
行けないよ。だってお金がないんだよ。
I can't go. But I don't have any money.
そんなこと言うなよ。だって彼は努力したんだ。
Don't say that. But he did try hard.
As a particle meaning 'even' or 'even X can/does' (e.g., '子どもだって分かる' = even children understand).
子どもだって分かる簡単な説明にしてください。
Please explain it simply so that even children can understand.
そんなこと、大人だって驚くよ。
Even adults would be surprised by that.
As a particle meaning 'also/too' to indicate inclusion (e.g., '私だって行きたい' = I want to go too).
彼女だって忙しいんだから、無理に誘わないほうがいい。
She's busy too, so you shouldn't insist on inviting her.
私だってそう思うよ。
I think so too.
Used colloquially to report hearsay ('I hear that...') or as a casual quotative/confirmation marker.
明日、休校だって。
I heard school is closed tomorrow.
彼、結婚するんだって？
You mean he's getting married?
天気予報では午後から雨だってさ。
The weather forecast says it'll rain from the afternoon.