Hi Lisa.
The phrase "diamond ring" is because before and after eclipse totality it really does look like a diamond ring - there is a thin semi-circle of sun light and a very bright "diamond" of light on one side.
Bailey's beads (the little bits of sunlight coming through craters at the Moon's edge just before and after totality) are named for the astronomer Francis Bailey (or maybe Baily - I am finding both spellings) . You can read more about him here:
http://en.wikipedia.org/wiki/Francis_Baily(I had to look that up, so now I've learned something from your question too!)
There are pictures of both the diamond ring effect and Bailey's beads here;
http://www.exploratorium.edu/eclipse/what2.htmlcheers,
Terry