Which icon on the Virtual Machine Connection toolbar functions like the Windows hibernation mode?

The icon that functions like the Windows hibernation mode is indeed the one that corresponds with the "Save" action. In the context of virtual machines, when you save a virtual machine's state, it effectively captures the current contents of the virtual machine's memory and preserves it to disk. This is similar to hibernation in Windows, which saves the current state of the operating system and all open applications to the hard drive, allowing it to resume later without losing any data or state.

Choosing the "Save" option allows users to pause their work without fully shutting down the virtual machine, allowing for a quicker start-up when they return. This is particularly useful for maintaining workflow and resource management, providing the flexibility to pause and resume operations much like hibernating a physical computer.