I will try to give a short answer to this. The three main layers of Cloud computing are as follows:
I. Infrastructure as a Service (IAAS): IAAS providers give low-level abstractions of physical devices. Amazon Web Services (AWS) is an example of IAAS. AWS provides EC2 for computing, S3 buckets for storage, etc. Mainly the resources in this layer are hardware like memory, processor speed, network bandwidth, etc.
II. Platform as a Service (PAAS): PAAS providers offer managed services like Rails, Django, etc. One good example of PAAS is Google App Engineer. These are the environments in which developers can develop sophisticated software with ease.
Developers just focus on developing software, whereas scaling and performance are handled by the PAAS provider.
III. Software as a Service (SAAS): SAAS providers offer an actual working software application to clients. Salesforce and Github are two good examples of SAAS. They hide the underlying details of the software and just provide an interface to work on the system. Behind the scenes, the version of Software can be easily changed.