A free allophone is that allophone of any phoneme for which no feature or articulatory movement is determined by its environment. By extension, an allophone may be said to be free with respect to any undetermined feature or phase even though some other of its features or phases may be determined.
It is partly a matter of terminology. It seems advantageous under certain circumstances, including the pedagogical, to use 'free' as the antonym of 'determined'. If one wants to press the concept of determination to such minute detail as to include all allophones, i.e. to say that no two realizations of a phoneme can be same except in identical environments, then 'determined' has no antonym. But there is ample precedent for drawing a line, perhaps best defined as that between perceptible and nonperceptible. The difference between the /w/s in a queen and chickweed is readily perceptible; the difference between the /k/s, if not so clearly hearable, is certainly perceptible in the proprioceptive sense of the observer's empathic analysis. The difference between the /w/s in a queen and between or in chickweed and shirtwaist is not, however, perceptible, nor, as a matter of labialization, that between the /k/s in a queen and a quart or in chickweed and backwards.