It's kind of like です or だ or だから but it sort of denotes that the person is a bit upset/angry/frustrated. It can sound a bit whiny/brat like (but some people think it's cute). It's mainly used by kids (or adults who speak in a childlike way). Eg. John: 「お前弱いな」 Jane: 「いいえ、あたし強いだもん」

「だから」という意味です。 私は強いだもん。 ＝ 私は強いだから。 また、だもんは口語しか使いません。

Thanks for clarifying :)

私は強いだもん is wrong. We don't say like that. You should say/write 私は強いんだもん. I'm strong, you know? 強い＋ん／の（particle）＋だ（auxiliary verb）＋もん／もの（particle ← noun） んだ／のだ is used that the sentence is concerned with another situation. son: 行ってきます。I go out. mother: いってらっしゃい。Have a nice day. （The son came back home at once） mother: どうしたの。What happened? son: 雨<あめ>が降<ふ>ってきたんだ。It has rained.（So I came back home once to take an umbrella with me.） ※んだ expresses that 雨が降ってきた is concerned with my coming back home＝reason. 私は強いんだもん is not the same as 私は強い. When someone uses 私は強いんだもん, he/she has things to prove it. If the speaker is a girl, she might remember the experience that she did not cry when she had preventive injection. ※もん expresses the feeling to emphasize. It's likeよ. Butもんhas also the meaning of the excuse (reason to justify oneself).