In the Village Proper area of Oerba is a tall building with some stairs leading up into it called the Dilapidated Dwelling. You can examine a number of items in this room using the Button, but the most important thing to do is to examine the small robot in the middle of the floor near the table.
This robot, named Bhakti, is involved in two side quests.
The first side quest involves helping to repair Bhakti by finding some spare parts in and around Oerba. The walkthrough page for Oerba points out where each of the spare parts is located. Repairing Bhakti will provide you with the following rewards:
Most of these rewards can be sold at one of the shops at a Save Stations and then, using the Gil that you receive, you can purchase the items required to upgrade your weapons.
Bhakti is also involved in some completionist tasks that are taken care of once you reach the end of the game. More specifically, Bhakti will be tracking all of the equipment you pick up, and if you haven’t picked up everything yet, it will state “…But somewhere out there, long-forgotten equipment still waits to be found!”. Unfortunately the little robot will never get more specific than that.
Talking to Bhakti is the last step you need to complete if you are looking to obtain the Treasure Hunter achievement / trophy. Check out the Treasure Hunter page for more information on how to complete this monumental task.