The flower is used as a symbol of the Austrian countryside and, in the context of the musical, as a symbol of home, Austria, and affection for the country.
One interesting little fact: the song wasn't actually an old Austrian folk song. It was written specifically for The Sound of Music by Richard Rodgers and Oscar Hammerstein II.
So the Edelweiss is actually a flower, not a person or a feeling. They grow in the mountains are very tough, a bit like daisies.
