One great way to look at a paradox is to compare it with other things. First, a paradox is not a contradiction. Contradictions simply are nonsense. No amount of reflection will get you anywhere. Second, a paradox is not a mystery. A mystery is something that cannot be explained. It is above reason.
A paradox is something that looks like a contradiction or a mystery on the surface, but under close reflection makes sense. There is a logic, but the logic is not apparent at first.
Here is an example from the New Testament: If you want to find your life, you must lose it.
Here is another example: The last shall be first and the first shall be last.
Here is a final example: To best way to be creative, is not to seek it.