In Client Server architecture there is one to one communication between client and server. Server is often at in-house datacenter and client can access same server from anywhere. If client is at a remote location, the communication can have high latency.
In Cloud Computing there can be multiple servers in the cloud. There will be a Cloud controller that directs the requests to right server node. In such a scenario clients can access cloud-based service from any location and they can be directed to the one nearest to them.
Another reason for Cloud computing architecture is high availability. Since there are multiple servers behind the cloud, even if one server is down, another server can serve the clients seamlessly.