Badass is a term associated with people who possess great prowess in physical fighting, bravery, durability, or mere coolness. The term is primarily used to describe either a type of character with these attributes or describe the kind of actions that a character performs.
However, exactly what a badass person or action is can differ wildly depending on context or the people using the term. This is shown in how it can be used as a noun or an adjective. While there is no precise definition, there is a broad consensus on actions or people who could often be called badass. A list of such properties is on the Analysis page.
See also Mary Sue, another fandom term that sees varied usage.