One of the reasons we have music is because there are feelings we have that cannot be expressed in words-only in music. If we could express all our feelings in words, we wouldn't need other art forms-dance, visual arts, etc.
Yet there are times when we need to communicate about music, using words. That is the purpose of music theory-it is a specialized language for discussing the characteristics and components of music.
Music consists of melody, harmony, rhythm, timbre, form, tempo, dynamics, and so forth-and within each one of these elements there are critical contrasts which create the feelings we have when listening to music. For example, many pieces of music have ABA form-they begin in one way, transition to another way, and return to the first way. A lot of second movements in symphonies have this form (which is called “song form”).
What is the meaning of ABA? You could liken it to a journey. You start somewhere, go somewhere different, and return where you started. How do you know when you have gotten to B? It is significantly different from A. If it just sounded like A, you would be in a static place, not on a journey. So, A has meaning because it contrasts with B in some way, and vice versa.
Or take dynamics, particularly those of Beethoven. Frequently he will have the performer crescendo and then drop suddenly into softness. The second movement of the Sonata Pathetique has this kind of moment in it (if you remember the radio show on classical music by Karl Haas, you'll know this movement because it was his theme song). In creating a crescendo, Beethoven creates some expectations in the ear of the listener-we are heading to a fortissimo. But then he surprises you with that sudden pianissimo. Again, the meaning comes about because forte and piano are opposites.
There are more complex forms of contrast and opposition in music, which is why we learn chord structures, scale forms, relationships between scales and chords, and ways of generalizing about all scales of a certain type. For example, we can derive seven chords from the standard major scale and we use numbers to refer to those chords. Those numbers are the same whether we are in F major or C# major.
It's not easy learning all those chords (and then the advanced versions of the chords-French this and Italian that), yet it is only through learning this vocabulary and its meaning that we can put into words at least a little of how music means. And we can use these words to help newer musicians learn to invest their playing or singing with as much meaning as possible.
Music more than anything is a meaningful form of communication. It's not about technique or competition-it is about sharing something from inside with another person or group of people. When we have words to talk about that, we can actually enhance our meaning-making with music. And that is the utility (and the fun) of music theory.