Stolen directly from Grigory M's question in the definition phase:
EDIT: As per Tsuyoshi Ito's correction (confirmed with a bit of googling), I've removed a misleading bit about the object of these verbs.
治す is only used to heal or to cure.
直す has more meanings, it can mean:
1) to fix; to correct; to repair;
2) to replace; to put back as it was;
3) to convert (into a different state); to transform;
その本をなおしなさい。= Put back the book where you found it.
次の文章を日本語に直しなさい。= Put the following sentences into Japanese.