In order to have a settlement, you have to have people who will manage and populate the area. It's good to have your settlements doing well because that deters outside forces from attacking, keeping everything and everyone there safe. You can highlight that settlement in the list to see what area needs attending too. If there is something that needs to be addressed, you will see a caution symbol next to the settlement name. If your settlement is doing well, you will simply see the settlement name in the list.
From here you can see the numbers of your settlements specs and more importantly if your settlement is doing well.
You can see the overview of your settlements from your Pip-Boy under Data > Workshops >. If you're looking for the pieces you need to build your new home, check out our huge guide to Crafting Components. Why grow a Settlement? In addition to the experience you gain from Crafting settlements and from recruiting missions, settlements attract traders, who in turn bring great gear and weapons to sell.