1To understand or comprehend; to grasp the meaning of something.
日本語の文法が少しずつ分かってきた。
I'm gradually starting to understand Japanese grammar.
彼の説明を聞いてようやく分かった。
After hearing his explanation, I finally understood.
この問題の意味が分かりますか？
Do you understand the meaning of this problem?
2To become clear or known; to be discovered or realized—used to indicate that something becomes evident.
彼がどこに行ったかはまだ分かっていない。
It is still not known where he went.
調査の結果、原因が分かった。
As a result of the investigation, the cause was found out.
3An interjection expressing agreement or empathy ('I know!' or 'I agree!').
A:『彼の気持ちが分かる』 B:『分かる！』
A: 'I understand how he feels.' B: 'I know!'
その説明、分かるよ。私も同じ経験がある。
I get that explanation. I've had the same experience.