To play rock music with great energy and enthusiasm, or to dance to rock music without inhibition.
"He put on his favourite album and rocked out alone in his bedroom for an hour."
Party on, Wayne. Party on, Garth.
— Wayne's World (1992 film) — the film's central theme of rocking out is encapsulated in this catchphrase, though the exact 'rock out' phrasing appears throughout the film.