[Glenn]

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 bottle making.