This is quite an old post, but since not all areas are covered I think adding some info. should be fruitful for future visitors.
Well, we've all been pretty wary when words like Unlimited were used in the past. But since the introduction of the cloud, it has become possible to offer near unlimited service. If you dig down to the architecture of a cloud platform, you'd realize that it's basically a cluster of multiple dedicated servers connected together in a network. All the resources of the individual dedicated servers are pooled together forming a large pool of resources. Depending on the virtualization tools used, it is possible to automatically assign and release the resources based on the requirements. For example if a particular website needs a certain volume of resources at a certain time during a day, the resources are borrowed from the large resource pool and then released back when it isn't required. It's a continuous process, so in a way you can say that you'd always find free resources on the cluster.
The price that you see on the website of a cloud service provider would be the price for registering the service with very little resources. If you use anything more than that, you'd be charged with certain price based on the resource that your site would actually consume. Therefore, it's important to check the TOS before signing up to get a better understanding of the service offering.