A work (book, article, image, painting, sculpture, movie, etc.) is in the public domain if it is not protected by intellectual property laws such as copyright, trademark, or patent laws. Speaking just about copyright, works pass into the public domain when the copyright is not renewed or expires, or when the creator intentionally places it into the public domain. This means that anyone can use a public domain work without obtaining permission.
Whether or not a work is protected by copyright depends on a number of factors including when it was created, where it was first published, whether it was published by a U.S. citizen, and its format. Works published in 1923, for example, may still be protected under certain circumstances. Sound recordings, for example, are subject to special conditions.
Don't confuse the public domain with public access. They have little to do with each other. A publicly accessible work available on the Internet, in a museum, or in a book may well be protected by copyright, and therefore not in the public domain.
And don't confuse the public domain with the need to cite your sources. This academic concept requires you to cite your sources regardless of whether they are copyrighted or in the public domain.
If there's a specific question on your mind, please let me know the details and I'll provide additional guidance.