Rose, that basically means "of their own rhythym". These monks may have work outside of the monastery and in general it is a much "looser" form of monasticism.
The monks may only meet for Matins, Vespers, or DL based on their "outside" work schedules and say the remainder of their prayer rule during the day while at their other tasks.
In ancient times they may have owned a piece of land to farm, etc. In today's parlance it would be more like owning your own car to go to work, etc. I think with the present conditions, the need to provide some sustenance for the new monastery or monastic community it may be worthwhile to look again at this type of life.
Historically there have been great and sometimes heated debates amongst monks who lived this way and the strictly cenobitic monks who lived in community according to a strict rule or monastic typikon and renounced all "outside" ownership and activities. That's what I was referring to earlier.
Rose, the "Bacon Priest" was Fr. Werenfried von Straaten of blessed memory, who was a great friend and supporter of the Greek Catholics being persecuted under Communism, and was a close personal friend of Patriarchs Josyp Slipij and Maximos IV Saigh.