You can close a case by closing all its workflows, meaning that you have moved each workflow to a step with a "closed" status. You can check a workflow's status by looking at the dot beside a workflow, which will be green when the workflow is closed. See Progress a Workflow to the Next Step for details on how to move a case through workflow steps. 

If a case has more than 1 workflow, the case is considered closed when the last workflow is moved to a “closed” status. The case in the example below has 2 workflows, called "Investigation" and "Status". "Investigation" is closed, but "Status" is open, so the case itself is still open. When both "Investigation" and "Status" are closed, the case will also be closed. 

Likewise, you can reopen a case by moving 1 of its workflows back to an "Open" status. Click the workflow timeline arrow and select another step.