The dictionary definitions are almost the same but the connotation is very different. Information is 'clear' when it is well understood. Information is 'obvious' when it is considered to be well understood also but the underlying tone is that obvious things are impossible not to understand.
For example if someone explains something to me and I say that it was 'clear' I mean that what they just said makes sense to me and I understand it. If I say that was 'obvious' I mean that the information was clear, I understood it, and likely that I already knew that and didn't really need the explanation.
Using the word 'clear' is a little more polite and objective than the word 'obvious'. Also as a question after some has finished explaining something they might say "Is/was that clear?" but no one would ever say "Is/was that obvious?".
Hope that helps! Keep learning :)