A quadratic equation is an equation that includes a squared term. For example, 3x + 7 = 28 is not a quadratic equation as it only has x, whereas x^2 + 5x + 6 = 0 is a quadratic equation as it includes x^2. Quadratic equations also usually have two solutions, whereas linear equations (like my first example) only have one.
I hope this helps! Let me know if you would like me to explain anything more :)