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I see two possibilities - that the event violates the laws of physics (as with walking on water), or that they are natural events that are possible within the laws of physics, but are simply very rare. The latter is rendered pretty much meaningless because such events would still be completely natural, and a supernatural event would be nothing special - a miracle would not be evidence of divinity, as they are commonly used, but as a case of luck or chance. The former meaning of supernatural is more complex.
To best understand this, I think we need to examine our reasons for accepting the laws of physics in the first place. Almost all of our scientific understanding of what can and can't happen comes from our observance in the past few thousand years of specific instances of certain events, the general conclusions (through the inductive method) that such observations lead to, and perhaps some other deductive rules that are implied by the inductive conclusions. We define the laws of physics based on what we have observed to have happened in the past. For example, we have always seen someone sink to the bottom of a deep body of water when they stood on it, so we conclude that people cannot walk on water, and time (further observations) have since in countless instances provided further backing for this rule. However, inductive conclusions are based only on those instances that have been observed so far, and not those that were unobserved, will happen in the future or are merely possible (this is the basic idea behind David Hume's famous problem of induction). This means that it is logically possible for an event to come along which breaks the previously perfect record and proves that the law is not true. This is an inherent property of the scientific method - its conclusions are revised as new data comes in. If something happens that has never happened before, that has always been considered impossible (because it has not happened before), then when it happens, I don't see it as an instance of the laws of physics being violated, but as evidence that the conclusions we treated as laws need to be revised. Thus the new data which goes against the old does not contradict nature or physics, just our current conception or system of such.
What this means is that any event that can happen (by this I mean, any event which can in some way at least theoretically be observed in some way or cause/change other events which are such) is natural; in fact, such things can be said to simply fall in the category of the earlier meaning of supernatural given above. The only thing left for supernatural events to be are things which could never be observed, could never in any way affect us. Such things could hypothetically take place in another universe, one that is completely separated from this one - that universe could even be the realm of a godly entity (or be the entity itself). However, such an entity could never have any effect, any bearing at all on our existence, else it would be a natural thing. So while supernatural things are logically possible, they are only so in such a way as to render them meaningless. We can posit countless, indeed infinite, possible supernatural things (for example, that our universe exists as the super-fast blink of a subatomic particle in some other unreachable metauniverse we can never interact with; or that each subatomic particle in our universe composes an entirely separate universe itself), but we have no reason to believe any of them is true, and such views are not in any way verifiable, and so they are meaningless.
And so the original two ways of looking at the word supernatural yielded nothing of substance. The only possibility I see left is that there are certain absolute natural physical laws to our universe (whether or not we know of them for sure right now), and supernatural events are events that do in fact happen (hypothetically observable to us) but which contradict these absolute laws. However, this attempt fails as well, since by definition the laws would no longer be absolute - for such absolutes to exist, supernatural events would not be logically possible. This seems to exhaust all the possible meanings for supernatural, all of which turn out useless.