A control variation is the base of the page, the one used as the initial design and the point of reference for future tests. If you were running A/B tests before Experiments were launched as a workflow, you will need to select one for each page.
The control variation is accessible through the main builder. To see and edit other variations, as well as do any other actions that concern them, create an experiment for that page in the Optimize >> Experiment tab.
Setting a control variation will not unpublish your other variations or cause any other kind of disruption.