About
What is music theory?
This topic, for most pupils, involves acquiring an understanding of the symbols encountered in a printed piece of music. For the more adventurous it may concern how harmonies (chords) and melodies work in certain key signatures; transposition, modulation and so on.
The phrase "music theory" is not normally a reference to the physics of acoustics, ie the theory of how sounds are made and function. So I suppose a better phrase would be "notation theory" when discussing how we write music down.
It makes you more independent of the teacher
Put simply, a basic understanding of how to read music (eg treble and bass clefs) enables you to pick up a piano or keyboard item in a music shop and work out the basics of whatever you want to play regardless of what styles you are working on with your teacher. The trouble is that some piano music has loads of dots! The amount of black ink can potentially put one off for life. This is why a careful teacher grades the music studied in lessons so that the pupil is NOT put off for life.
Classical Music and Theory
Classical music is possibly the genre for which an ability to read music is most desirable. There are loads of resources in music shops (and online) to help you: I would love to assist you along that path. You can sit a theory exam if you so wish but you don't have to. Very few bother going as far as that BUT if you wish to sit the grade 6 piano practical exam (ABRSM), you will need a pass in grade 5 theory (unless you wish to tackle "Practical Musicianship" grade 5 or Jazz Piano grade 5).