What is the green sponge at the bottom of arrangements that hold water?

It is called an oasis. This product is shipped dry and holds an amazing amount of water. It was developed in the 1950's for florists who, before that time, had used the glass "frog", chicken wire, and other such things to hold the flower stems in place. There are a couple of companies that make the product today, but Smitherman's is the oldest of the companies and coined the name Oasis.