I understand the basic cloud computing pyramid of SaaS,Paas, and IaaS layer.
So, PaaS layer runs above the IaaS layer and allows development of applications which can be offered as SaaS. The IaaS layer includes the hardware and the VMs.
Now, I have a doubt in mind when few people argue that some software whihc is to be SaaS is deployed on directly IaaS layer or on the PaaS layer.
As I understand that PaaS layer is just to provide the environment to develope the applications but if someone has a already built application then it is fair to say that the application will be deployed on the IaaS layer.
Is my understanding correct or needs some correction?
This is mostly true, but I would say the IaaS layer provides the physical or virtual machines, storage and other infrastructure services such as networking.
It depends. From my understanding you can deploy your application either to IaaS providers or PaaS providers. The choice depends on your needs and what suits you best. It is true that PaaS is often referred to be used for application development, but it can also be used to host your application.
A deployment to a PaaS provider does not require you to install and maintain the OS, databases, language runtimes and lots of other middleware. In comparison, if choosing an IaaS provider, you would have to take care of all those aspects yourself.
More sophisticated distinctions between IaaS, PaaS and SaaS are also described in quite a few topics here on Stackoverflow, for instance in What is SaaS, PaaS and IaaS? With examples