To level up a town, you have to do Sidequest missions (a teal blue sword or book icon) that are on or around the Town icon. Once you do two or three of them, this initial level up achievement will unlock.
Please note that more Town Sidequests will unlock as you progress through the Libra of Souls story missions. You must be right near the end of Chapter 4 or beginning of Chapter 5 for all Town Sidequests to appear.
Repeat these teal blue town Sidequests and you will level up the town multiple times. It will grow in size each time. You need to make it grow about 3 increments. The icon has two towers protruding to left and right on each side. At maximum you will see that it's about equal size as the large story area icons on the map.
Refrain from doing any Sidequest that says Bounty for Scoundels or In Search of Strength as these are optional and unrelated the Towns.