According to a tweet from Shuhei Yoshida, purchasing a PS4 game on your smartphone will cause the system to automatically boot up and begin downloading. Once the download is complete, the PS4 will once again go back to sleep.
This is most likely a response to the notoriously slow download speeds found on the PS3. Sony has vaguely mentioned the topic before, claiming that something better is incoming. But even on the networks worst days, this feature will hopefully help.