There's not a lot of deep, hidden symbolism in The Sound of Music. What you see is pretty much what you get.
One symbol is definitely explicit, though—edelweiss.
Edelweiss is a small white flower that's common in the Austrian mountains; it's almost considered the national flower. That strong association with the country is important to the captain. He sings a folksong about it, and one of the lyrics is "Bless my homeland forever."
In this film, edelweiss is really about home. The song makes its first appearance as the first song the captain sings in his own in front of the children, and it marks a hugely important transition in his relationship with them. He's gone from being totally shut down emotionally to agreeing to sing a sentimental for them. It's a transformative moment for everyone. The kids can't believe it.
(And, uh, neither can we.)
The captain sings it again during another important transition: when he's about to leave Austria to escape having to join the Nazi naval forces and live under the new regime. He gets the entire crowd at the Salzburg Festival singing along. It ends up being a small moment of resistance to the German occupation and affirmation of Austrian nationalism.
Way to stick it to the Nazis under the guise of just singing a pretty song for the audience.