"hands" on a clock, is the name for the two usually black pointers (arrows?) that rotate on a clock face. We call them the minute hand (the one that rotates faster and tells you the minutes) and the hour hand (the one that rotates slower and tells you the hour). So in this sentence it means that one of the pointers has fallen off the clock. Picture: https://s-media-cache-ak0.pinimg.com/564x/2d/a8/cc/2da8ccdcb03a4b8d5bb63821fe9ec5e3.jpg

If the sentence is "one of the hands has fallen off the church clock" then here's the breakdown. On a clock, there is an hour hand and a minute hand (and sometimes a seconds hand) that points the the numbers. One of the hands is talking about one of those three hands. And it has fallen off (no longer connected to) the clock (in the church)

"One of the hands has fallen off the church clock" makes more sense. If there is a group of objects, and from that group you take one, you are said to have "one of" the objects. It means that out from among, or "out of," that group of objects, you have taken one. So a clock normally has two hands (and sometimes a third second hand - second here is referring to a unit of time, not an ordinal number). If "one of," or "one out of" those two or three hands has fallen, then that means there is one or two hands remaining on the clock. I hope this makes sense.