This word means to understand, which might surprise you if you remember that the kanji 分 means "part" or "parts." Think of it this way: to understand something you have to break it down into its parts to see how it works.

Watch out, though, because whereas in English you understand something, in Japanese the thing you understand is the grammatical subject (it's doing the action). So, a more literal meaning for this is to be understandable. In other words, there's no object, and 分かる is intransitive, meaning it happens on its own. The かる ending is a hint, because verbs with かる as okurigana (kana added to the kanji) are usually intransitive.