It's an adverb derived from the adjective "sundara" (beautiful) and the suffix "-avagi" which indicates manner or way.
Here are some examples:
* Avala sundaravagi natisuttiddare. (She is dancing beautifully.)
* Idu sundaravagi kanuttide. (This looks beautiful.)
* Avaru sundaravagi paaduttaare. (They sing beautifully.)