Cloud for simple understanding can be considered as new way of thinking about system architecture, servers, and network bandwidth. Cloud computing is about "renting" resources vs purchasing hardware. You only pay for what you use and you are running your applications in someone else's data centers. For example Microsoft, Amazon, Google - they all have these data centers.
What are the core cloud services that are available?
- Compute - These can be the virtual machines or it could be a Windows or Linux server that runs in the cloud, can be a desktop or even a web application.
- Storage - File shares, databases or blob stores
- Networking services
- Application Services
You may have typically used all these services in the premises, but with cloud you would just pay for what you use.