In a traditional data center environment, a service runs on one server. You have one server for your website, another server for your customer database and so on. A traditional server environment is unreliable because if it fails, the service it provides becomes unavailable. A single server can't increase its performance during periods of high demand. In-house servers can also be costly to operate because you have to pay your own IT staff to maintain them.
In a cloud environment, a service doesn't reside on a single physical computer. It resides in a virtualized software-based environment that exists on many physical computers simultaneously. If one of the physical computers fails, the service doesn't go offline because it still exists on the other computers in the cloud data center.