Apparently someone thought this item was intended as a frame for pictures. The trimmed version, on the right, is about 8 inches square. While the hole is large enough to frame a small picture, there is no way to secure a picture to the frame. Nor is there any way to hang the frame or even to stand it. Along with the considerable weight and fragility of the pieces, it's unlikely they were made to hold pictures. Perhaps they were a sort of tile. Hard to say. In any event, there are very few around. The trimmed example shown here sold for $600 in 1995; another with rough spots sold in 2003 for $650. The untrimmed version above left, the only one known, brought $2,800 in 2003, $500 in 2007, and $525 in 2010.
UPDATE: Discovered to be a Tiffany tile. 1-10-20
Above is a souvenir piece in blue made for the 1976 International Carnival Glass Association convention in Indianapolis by Joe St Clair. It is also 8 inches square. This example sold for $45 in 2000. One sold on eBay in 2005 for $128.