The balloon driver, as others have pointed out, is used in an overcommit scenario as a way for the hypervisor to reclaim memory from a guest OS. There's a balloon driver loaded in to the guest which can communicate with the hypervisor. When the hypervisor needs more physical memory, it can ask a guest's balloon driver to inflate and start allocating physical memory pages. That will cause the guest to start reclaiming unused memory using it's native techniques; a Linux guest, for example, might destroy unused file buffer caches. The balloon driver can then release all the memory it's allocated and the guest won't bother reclaiming anything until it needs it.

I believe it's just memory overcommitment, so you can assign more memory than you actually have available on the host and it will dynamically handle it for you. Crazy stuff, though.

I think it means you can increase the RAM of a VM without shutting it down. With Xen, the VM needs to be rebuilt (a couple of minutes off)

Memory ballooning is basically a mechanism for hypervisor to steal pages from the guest and yes, so it allows for over-commitment. Memory balloon driver is present inside the guest and hypervisor communicates how many pages it needs back to the driver. The driver allocates pages and sends it back to the hypervisor.