A prophecy is, simply speaking, when something or someone states something unlikely will happen and it then happens... with no apparent connection to the original prediction. So a weatherman's prediction for the weather is not a prophecy; they have used a variety of techniques and knowledge of weather patterns to make an educated guess at upcoming weather. It's also not a prophecy if a person states they will kill you, and then later does... the statement and action are obviously connected in this case (and you should have called the police!).
I have two main criteria for an event to be considered a prophecy. First, the prediction needs to be reasonably clear about what is predicted; precise dates and details are not necessary, but the general prediction needs to give enough detail that it can be checked against the later event claimed to have been predicted. Second, the event predicted needs to either happen reasonably close to the initial prediction, or occur reasonably close to a predicted date or time. If this sounds vague, that's because prophecy as a category is often a vague set of events... often, the way the whole thing is interpreted is highly dependent on the people involved.
Oh, and prophecies should not be confused with curses, omens, or coincidences, even though all of these categories blend together some. Curses imply a future event will be caused by some mysterious means, whereas a prophecy simply states a future event will happen. Omens are events that are believed to foretell some form of ill-luck in the future, but they do not give specific details about those future events. Coincidences are separate events that seemingly are connected when they shouldn't be, and are only noticed after they happen... they give no form of foreknowledge, as prophecies claim to.