Before reading this page, it's recommended you have a read of Server Variables first. Configuration Variables are created and modified exactly the same way Project Variables are. The only difference is Configuration variables are only usable by the Configuration you create them in and can have their values changes whenever manually starting a build.
Configuration variables have an extra option when creating them, Prompt Type. If a prompt type is set, you will be required to supply a value for that variable when you manually start a build. The prompt type supplied determines the input field in which you supply the value.
Example 1 - Text Type/Boolean Prompt Type