Permanent Makeup is magic makeup that effects the recipients face and hair, and can last for few days, weeks, or possibly months. It was created by demigod children of Aphrodite and is impossible to remove in the time period that it lasts. It is considered a "curse" that Aphrodite's children can put on people who make them angry or a blessing that is established on children of Aphrodite when they are claimed.
When Piper McLean is claimed by her mother, Aphrodite, she is given a complete makeover, which is how Aphrodite's children are claimed. Every time Piper tries to get her hair down or remove the makeup on her face, it goes back to the way it was before. When complaining to some of the other members of the cabin, they tell her it will last anywhere from a few days to a few weeks (with much glee). Because of this, Aphrodite's blessing most likely involves the use of permanent makeup or a similar power of Aphrodite herself.