How you place your hands, bend your wrists, stretch your fingers and generally hold your instrument can greatly impact how you play it. Depending on the instrument, a simple bend of a wrist can lead you to consistently play out of tune, or make it hard for you to hit a specific note.

Even just touching strings in different ways can produce wildly different results; think playing a harmonic note on a bass guitar, which is how you get such a low-sounding instrument to play a high-pitched note. How you blow air through your horn can greatly change the timbre and mood of your music.

There are a lot more examples, and they are all difficult to correct if you aren't able to see what the musican is doing.