'Face the music' means accepting responsibility, even when the outcome is tough or uncomfortable. I cheated on the test, and now I have to face the music.
Pro Tip 2/3
Avoidance
This phrase often implies someone has been avoiding or delaying dealing with an unpleasant situation. He's been avoiding his creditors, but he'll have to face the music sooner or later.
Pro Tip 3/3
Emotional Weight
Using 'face the music' hints at a sense of dread or inevitability that comes with the situation. She had procrastinated long enough and was ready to face the music.