Being a server guy I see the 'cloud' as a hardware abstraction layer for software that has rapidly changing demands. If I need extra 'burst' processing capability for rare events, I can have a number of VM images on the cloud provider of the day ready to go at a moments notice. I don't have to have $x extra servers taking up space and power sitting unused 95% of the time.
I tend to think of my server room as baseline power, a nuclear power plant. I have a lot of power available, but it is inflexible if large, short endurance spikes of demand (it would take days to add new servers, even after I got purchase authorization). The cloud works like natural gas generators for me. They are more expensive to use, but they can be fired up quickly when needed and then shut down.
If it doesn't feel like a quantum leap in technology, maybe you aren't using it. VM/VDI has made deployment, management, and backup of servers click and drool easy. People where time sharing in the 60's because computers were expensive. I time share (VM) servers because they fast and cheap, so fast that without VMs you'd have to put a lot of services on one box, which in the Windows world is a great way to have things go bad.