Now suppose that same site (hosted on two dedicated machines) gets a sudden increase in traffic, beyond the capabilities of your two machines. Instead of reserving another dedicated machines, spool up a cloud instance (or two) to help handle the traffic, and once the traffic returns to normal, release the cloud instance(s).
Here's another possibility. Suppose you need 100 machines to crunch data for an hour. Launch 100 cloud server for that hour at their rate and you pay 100 x $0.15 = $10.50 for the hour instead of 100 x whatever they'll charge for a month of dedicated machine usage.
VPS, however, is actually more aligned to dedicated servers. Sure, because their hardware limits are manually imposed by virtualisation software, you can scale them, but generally that's designed for when you decide a server upgrade/downgrade is required, rather than on an ongoing basis to meet fluxtuating needs.
Essentially, the key difference between VPS and dedi is that VPS offers a cheaper solution if you want the flexibility of your own server without the cost of hardware that you don't need - as you can get cheap VPSs that give you full root access for $15/20 a month, a deal you'll never find with any dedicated server, regardless of its specifications.
(For my company's websites, we have ~20 quad core dedicated servers because we are able to handle a steady growth of traffic without the need of cloud servers, and we want complete control over them in a way that we wouldn't have with VPS servers. I have 5 VPS servers for personal use however, which lets me spread their power across four data centres in two continents, with various different uses for each of them, without the bill that a similar dedicated server setup would cost, as I don't really need huge amounts of CPU/RAM in each)