Most of the time when people refer to scholarly sources, they're referring to a certain type of articles and books.
Scholarly articles--which your professor may also call peer-reviewed, refereed, or academic articles--are considered the most reliable information sources. They are written by experts and go through a rigorous process where other subject experts analyze and critique the arguments to identify errors, faulty logic, and other problems. This process is called peer review, and while it's not foolproof, it does mean that these sources are likely to have the most trustworthy information on your topic.
Scholarly articles are:
Scholarly books share all of the characteristics of scholarly articles listed above, except one: instead of being subjected to the peer review process that articles undergo, they are instead reviewed by an editor.