Expense process status is an expense status that you can define and set. Each expense can be given an expense status based upon your business process. So you define what status's are required for your process. Note that expense process setup is only available for expenses that are separate from the timesheet. To understand this expense type click here.
To enable this setting and set your custom status's visit the following:
Menu SetupSettings Application Settings tab Expense Setup tab Expense Process Status tab
When the expense process status is on, you will see the process status on the expense screen and expense reports as per screenshots below.
You define which users should be able to change the process status. Note that the user will have the ability to change the expense status but only on expenses they have edit access defined in the permission screen below.