The Flows tab gives you a snap shot all the flows of your automation. It is set to have default views of active (people currently in an automation), completed, paused, stopped, and all.
Each view tells you the name of the automation and who the contact is. The last column in each tab allows you to perform an action either to pause, stop, restart, or reenter the automation.
On the Active tab you also have the option to "continue now" which will move the contact to the next stop in the automation.
The Flows tab is here to make it easier for you to see is in your automations and a quick way to control what is going on at the contact level without having to go to the contact directly. This is especially helpful if you have a group of contacts that you are going to be looking for to perform the same automation action to. To do this check the box to each name on any tab. At the top of the list you will see how many boxes are checked and an action box next to it that will allow you to perform a batch action.