• An inspired utterance of a prophet, viewed as a revelation of divine will.
• A prediction.

The first definition relies on a few things. Firstly, the person who says it has to be a prophet. Prophets are those who either speak through divine intervention (the word of God) or who are gifted with profound moral insight and exceptional powers of expression. I'm not so sure this would be true for Professor Trelawney, but it is generally thought that the prophecy she made in front of Harry and the one in front of Dumbledore are her only two prophecies. This is also stated by Dumbledore at the end of GOF.

The second definition raises a few questions. A prediction is not normally associated with divine inspiration and is based on evidence rather than supernatural goings on. Therefore, it may be that Trelawney's predictions are based on things she has seen in the past and so may not carry so much weight or be so accurate. On the other hand, it may be that she has more knowledge of Harry and the events that may happen than we think.

This brings us to the question of what a prophecy is in terms of its existence. It is widely considered that a prophecy is merely a way of us knowing what will happen in the future before it actually happens. If this is the case, then there seems no way that we could possibly change the course of a prophecy as it takes into account everything and anything that can and will happen and is a reflection of what will happen, not what will happen unless someone changes it. Working on this principle, we would say that after a prophecy is foretold, a chain of events will happen that will inevitably lead the people involved to the conclusion as stated in the prophecy.

This, however, raises the question of whether every event must have a prophecy and whether the knowing of the nature of the prophecy by the people involved will change anything. For the latter part, it seems that it will not as the revelation of the nature of the prophecy to the people involved is already accounted for in the prophecy, and the conclusion to the event will already include this. As for the former part, if only certain events have a prophecy, then surely any event that doesn't can be changed by any factor that happens to stop something happening or change the time of something etc. Dumbledore's words to Harry back this up: In COS, he tells him that it is our choices that make us who we really are, and he reiterates this in OOTP. This backs up the idea that not all events have a prophecy and that we can shape and mold them to change the future.

On the other hand, if every event did have a prophecy, then wouldn't our choices be accounted for in the outcome of the prophecy? This brings us to the point of who can say prophecies and who comes up with them? One possible explanation is that prophecies always exist in the very magical world that HP is set in, but some find their way into the bodies of "Seers" (like Trelawney) and thus they can recall them, which means there are only some that are able to recall them. It seems very unlikely that wizards themselves come up with the prophecy, as it would involve them having to look into the future (unless it was pot luck), which McGonagall already has said is very inaccurate.

So, a reliable conclusion could be that prophecies are all around us, perhaps not in physical form but in some form and that gifted people have the ability to turn the prophecy into words and to tell other people. It also seems fair to say that it is impossible to alter a prophecy as the prophecy takes into account any alterations that you will make to the future (this may be proven incorrect by the idea of choices in the HP world).