I discovered this on my kalanchoe awhile back. Very strange. You can even see some on the tips of the air roots. The tissue was firm, not moist or mushy.
I threw it all away for fear of it spreading. So far I haven't seen it again anywhere.
Don't know what you have but it looks like abnormal, uncontrolled growth. A little like what happens with the aloe mite, though from some other cause. Areas which were already in active growth kicked into overdrive. Some kind of virus maybe.
helenchild, To bad there wasn't some sort of county agent to ask or show a specimen to. It would be interesting to find out what it is, how to prevent it and so on. If you ever research further,make sure you let us know. Good luck, cll
From the looks of it, it would probably be classified as plant gall, which can be caused by many different organisms from wasps to fungi and bacteria.
The following website shows some of the many different appearances and provides some info as to the cause: