If two applications store data differently, but are constructed such that a file for one might possibly also be a valid (but meaningless) file for the other, very bad things can happen. A program may think it has successfully loaded the file (unaware that the data is meaningless) and then write back a file which to it would be semantically identical, but which would no longer be meaningfully readable by the application that wrote it (or anything else for that matter).
Using magic numbers doesn't entirely prevent this, but it can help at least somewhat.
BTW, trying to guess about the format of data is often very dangerous. For example, suppose one has a list of what are probably dates in the format nn-nn-nn. If one doesn't know what format the dates are in, there may be enough information to pretty well guess the format (e.g. if one of the records is 12-31-99, then absent information to the contrary, the dates are probably mm-dd-yy) but if all dates are within the first 12 days of a month, the data could easily be misinterpreted. Suppose, though, the data were preceded by something saying "MM-DD-YY". Then the risks of misinterpretation could be reduced.