Iaas, Paas, Saas are the major three major categories of cloud services.
IaaS (Infrastructure as a Service): Using Iaas, you can create your own virtual machines or storage, firewalls, load balancers, IP addresses, network, OS, etc. Iaas is an instant computing infrastructure available for you to use by paying for what you use.
Examples: Amazon EC2, Windows Azure, Rackspace, Google Compute Engine.
PaaS (Platform as a Service): provides an environment to build, test and deploy software applications. This includes OS, Programming language execution environment, database, web server, etc. You don’t have to maintain OS or any system updates.
Examples: AWS Elastic Beanstalk, Windows Azure, Heroku, Force.com, Google App Engine, Apache Stratos.
SaaS (Software as a Service): In the SaaS model, you will directly get the application from the vendor. You don’t even have to install the OS or the application and maintain it. You just have to pay and use it through some client.
Examples: Google Apps, Microsoft Office 365.
Let’s consider an example of creating a web application that stores data in a database.
With Iaas, you have to create the VM to install and configure the application, configure the network, create another VM and for the database (or get a database server from azure). You will end up creating multiple servers. Now, you are ready to access the application.
With Paas, you will get the VM with OS for the application, network and a database server as well. You just have to work on configuring the application. In most cases, you will directly get a link to access the database, not the whole server, which makes your job more easier.
With Saas, application is completely configured and is directly available to you.