What does "refining ignorance" mean? COuld you explain?
Although not the explicit goal, the best science can really be seen as refining ignorance. Scientists, especially young ones, can get too obsessed with results. Society helps them along in this mad chase. Big discoveries are covered in the press, show up on the university’s home page, help get grants, and make the case for promotions.

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'Refining ignorance' in this context means 'slightly reducing ignorance'.

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I believe this is saying the opposite of Ellie's answer.  The author's position (from this short passage) seems to be that today's scientists are bought off (via grant funding) to find a specific result or outcome.  By selling out science for research money, scientists are "refining" or perfecting ignorance.

I can't say for sure, though, without seeing more of this article.

However, the definition of 'refine' seems to support Ellie's answer.

http://learnersdictionary.com/definition/refine

Refine:
1.  to remove the unwanted substances in (something)
    refine oil/sugar

2. to improve (something) by making small changes

The inventor of the machine spent years refining the design.
    The class is meant to help you refine your writing style.