Electromagnetic waves originate from the acceleration of electric charges, often referred to as "wiggling charges." Maxwell's equations can be applied to derive the wave equation for both electric and magnetic fields, explaining how these waves propagate. For those seeking a clearer understanding, "A Student's Guide To Maxwell's Equations" by Fleisch is recommended as it introduces the necessary vector calculus. The discussion emphasizes the importance of understanding the fundamental principles behind electromagnetic wave generation. Overall, the conversation seeks clarity on the mechanisms producing these waves.