Materials in the public domain are items that are not protected under copyright, trademark, or patent laws. This means that you can use public domain materials for any purpose without requesting permission from a copyright holder.
Items typically enter the public domain either because the copyright holder relinquishes rights or because copyright protections have expired. Additionally, some materials - like federal publications - automatically go into the public domain because of the nature of the work.
Although terms have changed over time, currently copyright protections are in place for the life of the author plus 70 years. Once this time has elapsed, materials then enter the public domain for general use.
That said, it can be tricky determining if something is in the public domain--in no small part because copyright legislation has changed over time. In general, when you need to determine whether works fall into the public domain, consider the following:
To learn more, see this table by the Cornell Copyright Information Office. Stanford University Libraries also provide a helpful guide on copyright and the public domain.