1. Virtual computers/servers.
2. Data storage capacity.
3. Communications and messaging capacity.
4. Network capacity.
5. Development environments
In other words, Cloud Computing is for software developers, application vendors, savvy computer users, and corporate IT departments, not for people who use computer applications.
Take, for example, virtual computers. A virtual computer acts like a physical server, but is actually a program that runs on a much larger machine. It acts exactly like a physical computer - you can reboot it, load software on it - except that there is no actual hardware. To take advantage of Cloud Computing, you can go to Amazon and use their Amazon Web Services (AWS) Elastic Compute Cloud (EC2) service. What are you doing, exactly? You are essentially creating and renting one or more virtual servers that are running on Amazon's infrastructure. Instead of buying and installing, say, an IBM System x or HP ProLiant server, you tell Amazon to "instantiate" a virtual server for you. You pay by the hour, and by the amount of data stored.
Unless you work directly with your company's servers, you won't be the person actually working directly with Cloud Computing. Instead, your IT department may decide to use cloud services as the infrastructure to run applications on or to store data. Or, your software vendor could use cloud services like Google AppEngine or SalesForce.com's Force.com to build applications that then become "SaaS" applications.
That's primarily the difference: SaaS offerings are applications that are fully formed end-user applications. Cloud Computing is computing infrastructure and services that you can rent.
If you are in business, you will want to focus more on SaaS than cloud computing, unless your company develops software for a living.