In simple terms cloud hosting is done via a large high availability SAN (storage area network) with no single point of failure. This SAN is connected to big hypervisors (or you can call them the hardware nodes) that have a lot of CPU and RAM. Each hypervisor can host multiple VMs (Virtual Machines). The key of this whole setup is that SAN never goes down and if it does there is another one with mirrored copy which takes over. Having a single SAN is of no use so in cloud it must be fully redundant. And if a hypervisor goes down then based on available space the VM can automatically start off from another hypervisor. The data remains on the SAN so there is no delay of moving any data across servers. The CPU, RAM and disk allocation of VMs can be easily adjusted.
Now compare this to single server hosting solution where if the server crashes and the data is not recoverable you have to restore it all from the backup and many times re-setup the whole system from scratch, resulting in long downtimes. You cannot add more RAM, CPU or disk without downtime and there are physical limitations to it.