Freestyle refers to very specific sporting events, as well as a broader arena encompassing any sporting event; the former are extremely niche (listed below) while the latter can encompass any sporting event, provided it is operating in less than professional capacity.
Freestyle in general can refer to any sport where rules have been relaxed for this particular play; Freestyle is also used to directly express a few specific sports:
The art of freestyle walking (loosely related to free running) is a means of self-expression and creative interaction with one's environment. Freestyle walkers use leaps and air moves, clever footwork, dance or any non-traditional walking movement.
Freestyle wrestling is a style of amateur wrestling that is practiced throughout the world. Along with Greco-Roman, it is one of the two styles of wrestling contested in the Olympic games. It is, along with track and field, one of the oldest organized sports in history. American high school and college wrestling is conducted under different rules and is termed scholastic and collegiate wrestling.
The emphasis in freestyle is technical flat ground skateboarding. Often a freestyler will need little more than a board and a smooth, flat surface. Music and choreography have always been an essential part of the professional freestyle routine.
Freestyle is a category of swimming competition, defined by the rules of the International Swimming Federation (FINA), in which competitors are subject to only limited restrictions on their swimming stroke. (In other words, they have great freedom with respect to their swimming style.) The stroke used almost universally in freestyle races is the front crawl, as this style is generally the fastest. This swimming style is also the most common and has greater distances, such as 1500M or the 1650 yard swim. For this reason, the term freestyle is sometimes used as a synonym for front crawl