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In the world of Harry Potter, various wizards are described as being "powerful".
Harry had been a year old the night that Voldemort – the most powerful Dark wizard for a century, a wizard who had been gaining power steadily for eleven years – arrived at his house and killed his father and mother.
But how is wizardly power actually measured in the franchise? Is it just a matter of O.W.Ls and N.E.W.Ts or is there more to it?
TL;DR Magical ability is not measured in the Harry Potter universe (books or movies).
OWLs and NEWTs are academic achievements that measure the ability to perform useful tasks. Scores on these tests are used for career guidance and especially for admission to training programs and government jobs.
It is my belief that a measurement of magical ability would be about as useful as a measurement of IQ - an indication of potential, but not a prerequisite or even a predictor of actual success.
As far as I am aware, at no point in the books is a method of measuring the amount of magical power a wizard has ever mentioned. I found an interesting source after a Google search which has an interesting take on the matter:
The most accomplished wizards in the Potterverse are often described as elderly or hard-working. Voldemort began his reign of terror by the age of 40, but he had spent the previous twenty years working harder than anyone to become powerful. Horace Slughorn was already a teacher at Hogwarts in the late Thirties (and perhaps before), and he is described as an extremely able wizard who evaded Voldemort for one year (HBP4). Dumbledore is 150 years old and has spent most of his life studying. These wizards are powerful because they refined their abilities and amassed an extensive knowledge of magic, and because they had a lot of time to do it.
~http://www.hp-lexicon.org/essays/essay-magical-power.html
Thinking about it, I would agree that instead of differing amount of raw power possessed by individual wizards, the thing that differentiates the different levels of ability is being dedicated to improving and having a quick mind to respond to situations (such as in a duel, where fast - thinking is critical). Whether everyone has the ability to use all their magic power (for example, if they are mentally disabled) is a different matter.
If the amount of raw power differed from wizard to wizard, it would seem likely that pure bloods would be far more powerful than half-bloods or especially Muggle-borns. Hermione is often described as being "the best witch in the year", so this seems unlikely.
Like Muggle exams, OWLS and NEWTS are qualifications, and someone who is not very good at magic, but studied hard, would probably do better than a talented one that was complacent and did no revision.
