A scholarly, peer-reviewed source has been written by someone who is very knowledgeable about the subject (for example, a professor or other researcher), and has gone through an extra-rigorous kind of review by other experts (their peers). For an a source to be considered scholarly, those peers must agree that it is a good and valuable (but not necessarily irrefutable) piece of research. These sources are usually intended to be read by other experts or people studying the subject.
Popular resources are written for 'popular' consumption -- that is, to be accessible to most people. This might include newspapers or magazines, some books, and trade journals. While popular sources still (usually) go through a process of editing or review, it is less rigorous than the peer review process. Note that experts who are qualified to write scholarly articles can (and do) write popular sources, too. Popular sources can give you very good information, and can be the best sources to use for certain kinds of topics. However, we tend to use them differently than we would an academic source because of the type, depth and quality of information they include.
How can you tell if you have a scholarly article in your hand?
This chart outlines the basic things you should expect to see.
Some tips: