Academic, or scholarly, articles are articles published in academic journals that have undergone a peer review process. Academic articles are extensively researched and written by academics, who are often people like your professors!
Academic articles usually feature original research, whether it's an experiment or study the author(s) did, or a critical interpretation of a piece of media. You may also encounter academic articles that feature literature reviews, which explore the most influential pieces of writing on a topic.
Your professors will usually require that you use at least one academic article when you start writing research papers. Most of the databases have an option to limit the sources you see to academic journals or peer-reviewed sources. If you're not sure where to find this limiter, ask a librarian!