The Glass Cat was a glass statuette of a cat.
Catwoman wanted to steal the statuette from a Gotham City museum, but found someone else had beaten her to the loot. She chased the other thief, and in the end, knocked the thief down a rooftop window. She investigated, and found the statue broken on the floor. She also discovered a time machine, with which she traveled 15 minutes back in time.
Arriving before "the other thief", Catwoman managed to successfully steal the Glass Cat now, only to find out that the mystery thief she had been chasing was herself. She destroyed the time machine to get rid of her temporal double, and the backlash on the time-stream caused the statue to return to its original showcase, intact.