Mystery Solved!!!

   First, I want to thank everybody for your suggestions about this "Green Thing".  I followed all of them and compared what I had with the info and pictures that were available.
   Second, MyLifesMirror sent me to a link here in Florida that had pictures of exactly what I have growing in my yard.  Many, many thanks for all of everyone's help.

   This green thing is Oak Apple Gall.  It grows on oak trees.  It only occurs when a certain wasp lays eggs on the bark.  The egg causes the bark to send the signal to the bark to grow the gall, feeding the egg/gall at the same time through a stem.  They grow to 1 to 3" in diameter, are very green, with the a mildly textured edge.  It was named Apple because  1. looks somewhat like an apple,  2. turns redish,   3. is the size of an early-formed apple on an apple tree.   When the egg has developed, the wasp will burrow out of the gall, as seen on the picture.  In this case there were 2 eggs laid.  These pinpoint holes are very hard to see, and photographed with a macro lense to view them.  
   After the wasp is gone, the fruit changes color, and falls off the oak having caused no harm to the tree, ie a symbiotic relationship between the host and the insect.  I now have hundreds of them on the ground under the tree.  The extra is a pic of the gall and leaves that haven't been eaten by insects.
   All of this explains why I have so many acorns under the tree, but haven't seen the gall during the 6 years I have lived here.  This has been a great mystery, and all the more enjoyable when shared with the Blipfoto community.     Thank you, everyone.