You don't need to know how music works in order to play an instrument. You can pursue the pleasure and entertainment of performing classical music or songs for yourself or for others—even in the most moving, impassioned, fluent, and expressive form—without it being necessary to know theory, or to be able to compose.
Many students will choose not to go particularly deeply into how music works. And for good reason: it's hard work. If you're not planning to compose, and you're not passionately curious about why the music that you play and hear has the effect that it has on the human mind and heart, then a dedication to the study of the elements and harmony of music is unnecessary.
But you're still reading, so let's talk about the nature of music and how it compares to other forms of art.
The art of music has parallels in storytelling and joke-telling, to take just two examples. The ability to enjoy a good story or joke, or to be moved or interested by a good piece of music, is in each of us intuitively. Stories and jokes are told in everyday language, and familiar psychology. They are made of our conscious thoughts and desires and feelings, so we understand why they work. But music and rhythm work on a more primitive part of us: on the subconscious emotions, and their effects are as mysterious as those of love, scents, and rollercoasters. It's not apparent, and hard to put into words, why they affect us in the way they do. The ability to craft stories and jokes is not universal, and rarely intuitive. The ability to compose music intentionally (rather than by chance) is even further out of the reach of most of us.
In terms of its mysterious nature, music is arguably more closely related to abstract visual art, dance, and other abstract performance arts than it is to literary arts. But the mysterious nature of music does submit to persistent study. If you want to, you can learn what music means, how it functions, why it has the effects it has on us, and how to craft it. I can help you with that, and I refer you to the Elements and Harmony sections on this website, which contain reference and refresher material for a course of study with me.