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It is called a snap case. It's a bottle-making tool from the mid-1800s, and was used to hold onto the bottom of a wine bottle (note the cone in the center to accommodate the kick-up) while the neck was being finished with a lipping tool. It has wood-covered handles because they were used hot. The process is as follows: step 1: Blow glass into mold. Probably a three-part mold, judging by the deep kick-up. step 2: Open the mold, grab bottle with regular glass tongs, and fit snap case over the bottom. Squeeze to clamp. step 3: Reheat the neck, and use lipping tool to create the finished bottle. step 4: Release snap case, put bottle in annealing oven to cool slowly. There are several illustrations of these things floating around if you look into the history of bottlemaking.