godan verb (-su), intransitive verb
begin to dance; break into a dance
Describes the sudden start of dancing, often spontaneously or with energy.
音楽が流れると、彼女は踊り出した。
When the music started, she broke into a dance.
Variant with だす in kana; common in everyday writing.
踊る means 'to dance' in general, while 踊り出す specifically means 'to start dancing'.
Compound of 踊り (dance, continuative form of 踊る) + 出す (to start, to begin).