A work is in the public domain if its term of copyright protection is over, or if it never met the requirements for copyright protection in the first place. Works in the public domain can be used for any purpose without permission or licensing.
In the US, works published before 1923 have entered the public domain. Works published in other countries before 1923 may still be covered by US copyright. See ALA's digital copyright slider table for details on which works may be in the public domain. (When in doubt, ask permission to use these works.)
Most works created by the US federal government are not covered by copyright. Note that works created by state and local government can be covered by copyright (they may indicate they've been released to the public domain).