People often use the terms "author rights" and "literary rights" to mean copyrights. Copyrights are legal rights attached to intellectual property.
Although authors are the copyright owners of their scholarly work, your rights are taken when you sign away the rights to publishers during author agreements. Most author agreements transfer ALL copyrights to the publisher. It is important for you to read the author agreements/publisher agreements before signing an agreement with a publishers.
Why care about Author rights?
A complete transfer of author rights will result in:
it may prohibit you from depositing/publishing your work in a repository like PRISM
it may prohibit you from sharing your work with students, colleagues or professional organization
it may prohibit you from creating follow-up work or related research.
it may result in the publisher reusing your work without your permission/notice.