I know a couple of Artistic Director types who get many CD's sent their way with applications to play at their festivals. They may or may not choose performers on that basis. I would think that BIG NAMES are relatively well known and are hired for their pull (and have agents)
Word of mouth or having seen someone perform previously is another obvious way to get booked. If you snooze you lose, so get your name and music out there.
JohnB