A processor is essentially the "heart" of the desktop. When choosing which processor you need, the first things you need to look at are the requirements of the applications you will be using.
If you plan to use your desktop for general office work, using word processors, spreadsheets, PowerPoint, email and web browsing, a basic Dual Core processor, with a "clock speed" of around 2GHz will be more than sufficient.
If there are additional, specific applications you will be running, you will need to look at the system requirements.
Most software vendors list these on their website, and the information should be easily accessible (after all, software vendors want you to be able to use their software!) There will usually be "Minimum System Requirements"; this is the bare minimum level your desktop would need to be at for the application to work. There will also be "Recommended System Requirements", if you match this or exceed it, the application will then run to its full potential. We would always advise that you try to reach the "Recommended" level if possible, to ensure you get the best out of your software.