Answer: Music Theory" sounds like a bigger deal than it often is - you would think this would be a reference to theories of perception, how tones interact, etc. And sometimes it is, in advanced journals. But most commonly it just means instruction in reading standard notation and the naming of chords and intervals.

So, if you take Music Theory 101, you're generally going to be learning the nomenclature of intervals and chords, the reading of pitches in the various clefs, rhythm notation, what chords follow one another logically, and you might get so far as the study of voice-leading: techniques for managing polyphonic writing, i.e. counterpoint.

All of which really are valuable if you want to write your own music. There have been songwriters with such a natural gift for melody that they were able to come up with success by fiddling around by ear and getting someone else to write it down, but such people aren't that common. Most successful composers know how to write, just as most successful writers of novels are pretty good with grammar.

So: if you are Paul McCartney you might be able to make music without knowing what you're doing. But you'll be better off if you can handle notation and if you know the materials of harmony. All that is part of "music theory." My guess is that the knowledgeable composer has a longer career. Duke Ellington worked by ear at the time of his first composition, but then he studied harmony. He turned out pretty well.