Microsoft Dynamics CRM 2011 UI does not enable users to reactivate Activities. Once an activity such as Task is completed, it can not be re-opened, although users may add notes and attachments to it.
I can think of a business scenario in which a user is required to reactivate a Task. Maybe it is incomplete although reported as completed, or maybe reported completed by mistake.
In this scenario, a Process can be used as Processes can change completed Task state from ‘Completed’ to ‘Open‘. You can set a manual Workflow rule to do just that.