This is a bit misleading. One should ask the question why other languages don't have an equivalent term? Korea and Japan mainly use the term dao (do in japanese as in 'way of' that we also discussed in an earlier post); hapkido,karatedo, Aikido, judo. (Taikwando uses both: kwan is the same word as quan). In English we just say boxing, or fencing. We have different terms but not a category like quan.
As I've said elsewhere gongfu has many historic roots. The most important for explaining the meaning of quan is it's roots in village level trans-medium religion. There were cults to local deities, heroes, and ancestors. Each cult had a central shrine and an incense burner and as the cult grew, ashes from the original incense burner would be distributed to satellite shrines in other villages. Processional celebrations for each cult would travel between villages according to a ritual calender. This is one of the ways that villages renewed their ties of social order, commercial vigor, and mutual defense. Along a procession, depending on the nature of the particular cult, a village would sponsor a festival. These festivals were sometimes very complex and could last weeks. This created a kind of "unseen" or "celestial" extra-government or social order.
One common aspect of these festivals was performance. A standard thing to perform was a demonstration of your village's martial prowess. People were usually invited and paid to perform in other villages but when you performed in your own village you did it for free. What you performed was your village quan. So quan really means a traditional routine that demonstrates your village's prowess. Prowess was, of course, understood in terms of gongfu or accumulated merit.
It is still common in 2007 for a Chinese person in San Francisco to ask another Chinese person, "What is your home village?"
These festivals also had what we would call magic shows, circus arts, and theatrical performances that told religiously significant stories. Thus, gongfu and Chinese Opera are really different components of the a single tradition.