They seemed to be a group of peacefully living people, a sort of a religious commune. They were led by Ray, who, according to his own words, was a septon. Based on that it seems that they were building a small sept as the building in construction had a church-like appearance.
In fact this is all we know as there is no information about that in the books, because this plot doesn't appear there at all.
However in one of the Brienne's chapters from A Feast for Crows she is visiting a place called the Quiet Isle, which is a refuge for those sworn to the Faith of the Seven. Its penitents atone for their sins through contemplation, prayer, and silence.
Brienne talks there with the Elder Brother, who tells her how he found the Hound dying and was with him until his end. However some subtle details in his words suggest that in fact Sandor might have not died. Later, in the same place, she sees a novice monk, a gravedigger, who is hiding his face. All the above let the readers to speculate that the Hound lives and is in fact the gravedigger. This (quite solid) theory is described in details for example here and here.
Based on the above it seems that if the theory is correct (and since we now know that the Hound lives it almost certainly is) the commune is supposed to be based on the Quiet Isle, only extremely simplified.