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The criteria for a genuine miracle for the purposes of canonization are rigorous. They were set forth in the 1740s by Benedict XIV in response to Enlightenment dogmatic denial that miracles were possible. The criteria are strictly scientific and empirical. There are seven and I'll list as many as I can recall:

1. The cure must be complete

2. the cure must be lasting

3. the cure must be instantaneous (meaning, over a period of hours or a day or so, not over weeks or months

4. the patient must not have been treated for the illness or if any treatment was given, it must not have been intended or expected to have cured the illness--e.g., someone whose was in intense pain and terminally ill might have been given morphine to control pain but then he recovers fully, suddenly and lastingly from the cancer that was killing him

5. the disease must be one for which no cure is known

I don't remember the other two. But the point should be clear--if there's any possbility of explaining the cure by medical or natural means, the supposed miracle doesn't count. For instance, ruling out cures that take place slowly eliminates uncontrolled variables: if someone recovered from cancer over a period of months, even though he was not receiving any cancer treatment, still, there could have been some shift in his diet or in his surroundings or who knows what that hiddenly contributed to his cure. The Church doesn't want any contamination from unknown sources for a cure, so she specifies that the cure has to take place within a few hours so that the time period during which extraneous variables might have acted on the patient is cut down to almost nothing.

To give an example of the completeness criterion: a boy who was blind because of an atrophied optic nerve was taken to Lourdes and bathed in the water. Suddenly he began to see. This meets the sudden/spontenous cure criterion and after his ability to see lasted for years, he met the "lasting" criterion. But when they examined him afterwards, his optic nerve remained atrophied as before. Therefore, this does not count as one of the 60 or so approved miracles of Lourdes (the latest was just approved a day or two ago). Tens of thousands of cures at Lourdes have been alleged and only 65 or so meet all 7 criteria. That the boy with the atrophied optic nerve could see is certainly a miracle in the common understanding of the word, but because it was not complete, because the nerve was still damaged and not functioning (he was somehow able to see without going through the optic nerve), this miracle is not an official one, merely an unofficial one.

In the case of the nun cured of cancer by JPII's intercession, if she was receiving chemotherapy or any other cancer treatment, it won't count. Presumably she was not or the people around her wouldn't be trumpeting this--or perhaps they don't know the criteria.

This is the difference between Catholic official miracles and the charismatic healing ministry claims another poster referred to. There are indeed tens of thousands of alleged miracles reported by Catholics every year. But many of these can never be proven one way or another because no careful, clinical observations before or after or both were preserved--the observations are informal and, while those who saw what happaned may be convinced a miracle took place (and it might have), the Catholic Churc requires, preferably, medical miracles in which a full record of scientific, clinical observations have been recorded both before and after.