It mostly has to do with transitivity. 分かる is an intransitive verb, whereas 書く is transitive. Generally speaking, you use を with transitive verbs, and が with intransitive verbs. This isn't always the case; を and が can sometimes be interchangeable depending on the level of "volition" with regards to the action. を might suggest that the action was willing, while が might suggest that the action was unwilling, etc... This link explains it a lot better than I can, though. Check it out: http://www.imabi.net/l111gavswo.htm

In a ・は・が sentence, 分かる has the meaning of "to be understood", "to be comprehensive". A similar case is 好き. You don't like something, but something "is liked". Therefore Xが分かる means "X is comprehensive" / "to understand X".