Freestyle is a way of dancing in which the dancer improvises his moves on the spot, as he dances, instead of having them planned beforehand (ie choreography). In its most extreme form it is the very opposite of choreography, however it can be argued that such an extreme level can never be reached, as we all to some degree plan our moves beforehand. To give an example, one might put on a piece of music and start freestyle dancing to it, but having heard the piece before, and having practiced different moves earlier, one can never 100% freestyle to it. This can be seen in many freestyle dance competitions where dancers, although ostensibly freestyle dancing, still perform trademark moves or sequences they've practiced earlier.
Not to be confused with All-Style dancing, in which different dance styles are mixed.