Safe Harbor Hours
According to this FCC page, shows with "indecent and profane content" may be aired between 10:00pm and 6:00am. "Obscene content" is still prohibited at all times, however.
Broadcasting obscene content is prohibited by law at all times of the day. Indecent and profane content are prohibited on broadcast TV and radio between 6 a.m. and 10 p.m., when there is a reasonable risk that children may be in the audience.
The term "safe harbor" refers to the hours during which broadcasters may transmit material deemed indecent for children. This "safe harbor", enforced by the Federal Communications Commission, extends—legally—from 10 PM to 6 AM and was established by the US Supreme Court case FCC v. Pacifica. This "safe harbor" is based on evidence that children 17 years of age and under are less likely to be in the audience during these hours. Sexual content and foul language are lawfully channeled to times of the day when children are less likely to be in the broadcast audience.
Here is an example Safe Harbor audio announcement from XRAY.fm in Portland, Oregon.
"Between the hours of 10pm and 6am, KXRY may broadcast material that could be found offensive to some members of our audience. Listener discretion is advised."